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1.

図書
図書
1. Global Lorentzian geometry
John K. Beem, Paul E. Ehrlich
出版情報: New York : M. Dekker, c1981  vi, 460 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 67
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2.

図書
図書
2. Differential geometry and its applications
edited by D. Krupka and A. Švec
出版情報: Dordrecht ; Tokyo : D. Reidel , Brno : J.E. Purkyně University , Norwell, MA : Distributors for the U.S.A. and Canada, Kluwer Academic Publishers, c1987  xiii, 379 p. ; 25 cm
シリーズ名: Mathematics and its applications ; East European series
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3.

図書
図書
3. Differential geometry
Tanjiro Okubo
出版情報: New York : M. Dekker, c1987  xviii, 788 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 112
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4.

図書
図書
4. Geometric inequalities (: U.S. ; : Germany)
Yu.D. Burago, V.A. Zalgaller ; translated from the Russian by A.B. Sossinsky
出版情報: Berlin ; Tokyo : Springer-Verlag, c1988  xiv, 331 p. ; 24 cm
シリーズ名: Springer series in Soviet mathematics
Die Grundlehren der mathematischen Wissenschaften ; 285
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5.

図書
図書
5. Symplectic techniques in physics
Victor Guillemin, Shlomo Sternberg
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1984  xi, 468 p. ; 24 cm
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目次情報: 続きを見る
Preface
Introduction / I：
Gaussian optics / 1：
Hamilton's method in Gaussian optics / 2：
Fermat's principle / 3：
From Gaussian optics to linear optics / 4：
Geometrical optics, Hamilton's method, and the theory of geometrical aberrations / 5：
Fermat's principle and Hamilton's principle / 6：
Interference and diffraction / 7：
Gaussian integrals / 8：
Examples in Fresnel optics / 9：
The phase factor / 10：
Fresnel's formula / 11：
Fresnel optics and quantum mechanics / 12：
Holography / 13：
Poisson brackets / 14：
The Heisenberg group and representation / 15：
The Groenwald-van Hove theorem / 16：
Other quantizations / 17：
Polarization of light / 18：
The coadjoint orbit of a semidirect product / 19：
Electromagnetism and the determination of symplectic structures / 20：
Epilogue: Why symplectic geometry?
The geometry of the moment map / II：
Normal forms / 21：
The Darboux-Weinstein theorem / 22：
Kaehler manifolds / 23：
Left-invariant forms and Lie algebra cohomology / 24：
Symplectic group actions / 25：
The moment map and some of its properties / 26：
Group actions and foliations / 27：
Collective motion / 28：
Cotangent bundles and the moment map for semidirect products / 29：
More Euler-Poisson equations / 30：
The choice of a collective Hamiltonian / 31：
Convexity properties of toral group actions / 32：
The lemma of stationary phase / 33：
Geometric quantization / 34：
Motion in a Yang-Mills field and the principle of general covariance / III：
The equations of motion of a classical particle in a Yang-Mills field / 35：
Curvature / 36：
The energy-momentum tensor and the current / 37：
The principle of general covariance / 38：
Isotropic and coisotropic embeddings / 39：
Symplectic induction / 40：
Symplectic slices and moment reconstruction / 41：
An alternative approach to the equations of motion / 42：
The moment map and kinetic theory / 43：
Complete integrability / IV：
Fibrations by tori / 44：
Collective complete integrability / 45：
Collective action variables / 46：
The Kostant-Symes lemma and some of its variants / 47：
Systems of Calogero type / 48：
Solitons and coadjoint structures / 49：
The algebra of formal pseudodifferential operators / 50：
The higher-order calculus of variations in one variable / 51：
Contractions of symplectic homogeneous spaces / V：
The Whitehead lemmas / 52：
The Hochschild-Serre spectral sequence / 53：
Galilean and Poincare elementary particles / 54：
Coppersmith's theory / 55：
References
Index
Preface
Introduction / I：
Gaussian optics / 1：
6.

図書
図書
6. Introduction to complex hyperbolic spaces (: U.S. ; : Germany)
Serge Lang
出版情報: New York : Springer-Verlag, c1987  viii, 271 p. ; 25 cm
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7.

図書
図書
7. Differential geometry and topology
A.T. Fomenko ; translated from Russian by D.A. Leites
出版情報: New York : Consultants Bureau, c1987  xiii, 323 p. ; 24 cm
シリーズ名: Contemporary Soviet mathematics
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8.

図書
図書
8. Geometrical methods of mathematical physics (: pbk)
Bernard F. Schutz
出版情報: Cambridge ; New York : Cambridge University Press, 1980  xii, 250 p. ; 24 cm
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目次情報: 続きを見る
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
Mappings / 1.2：
Real analysis / 1.3：
Group theory / 1.4：
Linear algebra / 1.5：
The algebra of square matrices / 1.6：
Bibliography / 1.7：
Differentiable manifolds and tensors / 2：
Definition of a manifold / 2.1：
The sphere as a manifold / 2.2：
Other examples of manifolds / 2.3：
Global considerations / 2.4：
Curves / 2.5：
Functions on M / 2.6：
Vectors and vector fields / 2.7：
Basis vectors and basis vector fields / 2.8：
Fiber bundles / 2.9：
Examples of fiber bundles / 2.10：
A deeper look at fiber bundles / 2.11：
Vector fields and integral curves / 2.12：
Exponentiation of the operator d/d[lambda] / 2.13：
Lie brackets and noncoordinate bases / 2.14：
When is a basis a coordinate basis? / 2.15：
One-forms / 2.16：
Examples of one-forms / 2.17：
The Dirac delta function / 2.18：
The gradient and the pictorial representation of a one-form / 2.19：
Basis one-forms and components of one-forms / 2.20：
Index notation / 2.21：
Tensors and tensor fields / 2.22：
Examples of tensors / 2.23：
Components of tensors and the outer product / 2.24：
Contraction / 2.25：
Basis transformations / 2.26：
Tensor operations on components / 2.27：
Functions and scalars / 2.28：
The metric tensor on a vector space / 2.29：
The metric tensor field on a manifold / 2.30：
Special relativity / 2.31：
Lie derivatives and Lie groups / 2.32：
Introduction: how a vector field maps a manifold into itself / 3.1：
Lie dragging a function / 3.2：
Lie dragging a vector field / 3.3：
Lie derivatives / 3.4：
Lie derivative of a one-form / 3.5：
Submanifolds / 3.6：
Frobenius' theorem (vector field version) / 3.7：
Proof of Frobenius' theorem / 3.8：
An example: the generators of S[superscript 2] / 3.9：
Invariance / 3.10：
Killing vector fields / 3.11：
Killing vectors and conserved quantities in particle dynamics / 3.12：
Axial symmetry / 3.13：
Abstract Lie groups / 3.14：
Examples of Lie groups / 3.15：
Lie algebras and their groups / 3.16：
Realizations and representations / 3.17：
Spherical symmetry, spherical harmonics and representations of the rotation group / 3.18：
Differential forms / 3.19：
The algebra and integral calculus of forms / A：
Definition of volume -- the geometrical role of differential forms / 4.1：
Notation and definitions for antisy mmetric tensors / 4.2：
Manipulating differential forms / 4.3：
Restriction of forms / 4.5：
Fields of forms / 4.6：
Handedness and orientability / 4.7：
Volumes and integration on oriented manifolds / 4.8：
N-vectors, duals, and the symbol [epsilon][subscript ij...k] / 4.9：
Tensor densities / 4.10：
Generalized Kronecker deltas / 4.11：
Determinants and [epsilon][subscript ij...k] / 4.12：
Metric volume elements / 4.13：
The differential calculus of forms and its applications / B：
The exterior derivative / 4.14：
Notation for derivatives / 4.15：
Familiar examples of exterior differentiation / 4.16：
Integrability conditions for partial differential equations / 4.17：
Exact forms / 4.18：
Proof of the local exactness of closed forms / 4.19：
Lie derivatives of forms / 4.20：
Lie derivatives and exterior derivatives commute / 4.21：
Stokes' theorem / 4.22：
Gauss' theorem and the definition of divergence / 4.23：
A glance at cohomology theory / 4.24：
Differential forms and differential equations / 4.25：
Frobenius' theorem (differential forms version) / 4.26：
Proof of the equivalence of the two versions of Frobenius' theorem / 4.27：
Conservation laws / 4.28：
Vector spherical harmonics / 4.29：
Applications in physics / 4.30：
Thermodynamics
Simple systems / 5.1：
Maxwell and other mathematical identities / 5.2：
Composite thermodynamic systems: Caratheodory's theorem / 5.3：
Hamiltonian mechanics
Hamiltonian vector fields / 5.4：
Canonical transformations / 5.5：
Map between vectors and one-forms provided by [characters not reproducible] / 5.6：
Poisson bracket / 5.7：
Many-particle systems: symplectic forms / 5.8：
Linear dynamical systems: the symplectic inner product and conserved quantities / 5.9：
Fiber bundle structure of the Hamiltonian equations / 5.10：
Electromagnetism / C：
Rewriting Maxwell's equations using differential forms / 5.11：
Charge and topology / 5.12：
The vector potential / 5.13：
Plane waves: a simple example / 5.14：
Dynamics of a perfect fluid / D：
Role of Lie derivatives / 5.15：
The comoving time-derivative / 5.16：
Equation of motion / 5.17：
Conservation of vorticity / 5.18：
Cosmology / E：
The cosmological principle / 5.19：
Lie algebra of maximal symmetry / 5.20：
The metric of a spherically symmetric three-space / 5.21：
Construction of the six Killing vectors / 5.22：
Open, closed, and flat universes / 5.23：
Connections for Riemannian manifolds and gauge theories / 5.24：
Introduction / 6.1：
Parallelism on curved surfaces / 6.2：
The covariant derivative / 6.3：
Components: covariant derivatives of the basis / 6.4：
Torsion / 6.5：
Geodesics / 6.6：
Normal coordinates / 6.7：
Riemann tensor / 6.8：
Geometric interpretation of the Riemann tensor / 6.9：
Flat spaces / 6.10：
Compatibility of the connection with volume-measure or the metric / 6.11：
Metric connections / 6.12：
The affine connection and the equivalence principle / 6.13：
Connections and gauge theories: the example of electromagnetism / 6.14：
Solutions and hints for selected exercises / 6.15：
Notation
Index
Appendix
Preface
Some basic mathematics / 1：
The space R[superscript n] and its topology / 1.1：
9.

図書
図書
9. Gauge field theory and complex geometry (: us ; : gw)
Yuri I. Manin ; translated from the Russian by N. Koblitz and J.R. King
出版情報: Berlin ; New York : Springer-Verlag, c1988  x, 295 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 289
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10.

図書
図書
10. Differential Galois theory
J.F. Pommaret
出版情報: New York : Gordon and Breach Science Publishers, c1983  viii, 759 p. ; 24 cm
シリーズ名: Mathematics and its applications ; v. 15
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11.

図書
図書
11. Elliptic operators, topology and asymptotic methods (: uk ; : us)
John Roe
出版情報: Harlow, Essex : Longman Scientific & Technical , New York, NY : J. Wiley & Sons, 1988  184 p. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 179
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12.

図書
図書
12. Geometric quantization
by Nicholas Woodhouse
出版情報: Oxford : Clarendon Press, 1980  xi, 316 p. ; 24 cm
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目次情報: 続きを見る
Symplectic Geometry / 1：
Lagrangian and Hamiltonian Mechanics / 2：
Symmetry / 3：
Hamilton-Jacobi Theory / 4：
Complex Polarizations / 5：
Elementary Relativistic Systems / 6：
Classical Fields / 7：
Prequantization / 8：
Quantization / 9：
The Metaplectic Correction / 10：
Symplectic Geometry / 1：
Lagrangian and Hamiltonian Mechanics / 2：
Symmetry / 3：
13.

図書
図書
13. The penrose transform : its interaction with representation theory
Robert J. Baston and Michael G. Eastwood
出版情報: Oxford : Clarendon Press , New York ; Tokyo : Oxfrod University Press, 1989  xv, 213 p. ; 24 cm
シリーズ名: Oxford mathematical monographs
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目次情報: 続きを見る
Introduction / 1：
Lie Algebras and Flag Manifolds / 2：
Homogeneous Vector Bundles on G/P / 3：
The Weyl Group, its Actions, and Hasse Diagrams / 4：
The Bott-Borel-Weil Theorem / 5：
Realizations of G/P / 6：
The Penrose Transform / 7：
The Bernstein-Gelfand-Gelfand Resolution / 8：
The Penrose Transformation in Practice / 9：
Constructing Unitary Representations / 10：
Module Structures on Cohomology / 11：
Conclusion and Outlook / 12：
Introduction / 1：
Lie Algebras and Flag Manifolds / 2：
Homogeneous Vector Bundles on G/P / 3：
14.

図書
図書
14. Geometry of classical fields
Ernst Binz, Jędrzej Śniatycki, Hans Fischer
出版情報: Amsterdam ; Tokyo : North-Holland , New York : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988  xviii, 450 p. ; 25 cm
シリーズ名: North-Holland mathematics studies ; 154
Notas de matemática ; 123
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15.

図書
図書
15. Topics in physical geometry
Robert Hermann
出版情報: Brookline, Mass. : Math Sci Press, c1988  xv, 595 p. ; 24 cm
シリーズ名: Interdisciplinary mathematics ; v. 24
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16.

図書
図書
16. Symplectic geometry
A.T. Fomenko ; translated from the Russian by R.S. Wadhwa
出版情報: New York ; Tokyo : Gordon and Breach, c1988  xiii, 387 p. ; 24 cm
シリーズ名: Advanced studies in contemporary mathematics ; v. 5
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17.

図書
図書
17. Methods of differential geometry in analytical mechanics
Manuel de León, Paulo R. Rodrigues
出版情報: Amsterdam ; Tokyo : North-Holland, 1989 , New York, N.Y., U.S.A. : Distributors for the U.S.A. and Canada, Elsevier Science Pub Co., 1989  x, 483 p. ; 25 cm
シリーズ名: North-Holland mathematics studies ; 158
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18.

図書
図書
18. Modern differential geometry for physicists (: pbk. ; : hdc.)
Chris J. Isham
出版情報: Singapore ; Teaneck, N.J. : World Scientific, c1989  vii, 182 p. ; 23 cm
シリーズ名: World Scientific lecture notes in physics ; v. 32
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19.

図書
図書
19. Geometry of manifolds
edited by K. Shiohama
出版情報: Boston ; Tokyo : Academic Press, c1989  xv, 517 p. ; 24 cm
シリーズ名: Perspectives in mathematics ; v. 8
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目次情報: 続きを見る
Dynamical Systems and Geometry
Applications of Nonstandard Analysis to Stochastic Flows and Heat Kernels on Manifolds / H. Akiyama
Hamiltonian Structure and Formal Complete Integrability of Third-Order Evolution
Equations of Not Normal Type / Y. Watanabe
The Quasi-Classical Calculation of Eigenvalues for the Bochner-Laplacian on a Line Bundle / A. Yoshioka
Geometry of Submanifolds and Tensor Geometry
The Dirichlet Problem at Infinity for Harmonic Mappings between Hadamard Manifolds / K. Akutagawa
Oriented 6-Dimensional Submanifolds in the Octonians: II / H. Hashimoto
Notes on Tricerri-Vanhecke's Decomposition of Curvature Tensors / T. Kashiwada
The Structure of the Symmetric Space with Applications / T. Nagano ; M. Sumi
On Some Compact Almost K*adahler Manifolds with Constant Holomorphic Sectional Curvature / T. Sato
On the Rigidity and Homogeneity for K*adahler Submanifolds of Complex Space Forms / Y. Taniguchi
Harmonic Non-Holomorphic Maps of 2-Tori into the 2-Sphere / M. Umehara ; K. Yamada
Lie Sphere Geometry
Wave Equation and Isoparametric Hypersurfaces / J. Kaneko
Construction of Taut Embeddings and Cecil-Ryan Conjecture / R. Miyaoka ; T. Ozawa
Lie Contact Manifolds / H. Sato ; K. Yamaguchi
On Simple Graded Lie Algebras of Finite Depth / T. Yatsui
Riemannian Geometry
On Decompositions of Riemannian Manifolds with Nonnegative Ricci Curvature / R. Ichida
p-Convex Domains in Rn / J.-i. Itoh
Geodesic Spheres and Poles / M. Maeda
Topology of Complete Open Manifolds with Non-Negative Ricci Curvature / Y. Otsu
On the Isodiametric Inequality for the 2-Sphere / T. Sakai
An Isoperimetric Problem for Infinitely Connected Complete Open Surfaces / K. Shiohama ; M. Tanaka
Positively Curved Manifolds with Restricted Diameters / T. Yamaguchi
The Ideal Boundaries of Complete Open Surfaces Admitting Total Curvature c(M) = -(infinity) / T. Shioya
On the Lengths of Stable Jacobi Fields
The Geometry of Laplace Operators
Riemannian Manifolds p-Isospectral but Not (p+1)-Isospectral / A. Ikeda
On the Holomorphicity of Pluriharmonic Maps / H. Naito
On the Instability of Minimal Submanifolds and Harmonic Maps / T. Okayasu
Yang-Mills Connections
Compactifying the Moduli Space of 1-Instantons on HPn / H. Doi ; T. Okai
Spectra of Riemannian Manifolds Without Focal Points / H. Urakawa
Based Anti-Instantons and Gravitational Instantons / M. Itoh
The 2- / Y. Kamiyama
Dynamical Systems and Geometry
Applications of Nonstandard Analysis to Stochastic Flows and Heat Kernels on Manifolds / H. Akiyama
Hamiltonian Structure and Formal Complete Integrability of Third-Order Evolution
20.

図書
図書
20. Groups and geometric analysis : integral geometry, invariant differential operators, and spherical functions
Sigurdur Helgason
出版情報: Orlando ; Tokyo : Academic Press, 1984  xix, 654 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 113
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21.

図書
図書
21. Geometric theory of foliations (: us ; : sz)
César Camacho, Alcides Lins Neto ; translated by Sue E. Goodman
出版情報: Boston, MA ; Basel : Birkhäuser, c1985  205 p. ; 24 cm
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22.

図書
図書
22. Spinor and twistor methods in space-time geometry (pbk)
Roger Penrose, Wolfgang Rindler
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1986  ix, 501 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Spinors and space-time ; Vol. 2
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目次情報: 続きを見る
Preface
Summary of volume 1
Twistors / 6：
Null congruences / 7：
Classification of curvature tensors / 8：
Conformal infinity / 9：
Appendix
References
Subject and author index
Index of symbols
Preface
Summary of volume 1
Twistors / 6：
23.

図書
図書
23. Differential geometry : manifolds, curves, and surfaces (: us ; : gw)
Marcel Berger, Bernard Gostiaux ; translated from the French by Silvio Levy
出版情報: New York ; Berlin ; Tokyo : Springer-Verlag, c1988  xii, 474 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 115
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目次情報: 続きを見る
Background
Differential Equations
Differentiable Manifolds
Partitions of Unity, Densities and Curves
Critical Points
Differential Forms
Integration of Differential Forms
Degree Theory
Curves: The Local Theory
Plane Curves: The Global Theory
A Guide to the Local Theory of Surfaces in R3
A Guide to the Global Theory of Surfaces
Bibliography
Index of Symbols and Notations
Index
Background
Differential Equations
Differentiable Manifolds
24.

図書
図書
24. Two-spinor calculus and relativistic fields (: pbk)
Roger Penrose, Wolfgang Rindler
出版情報: Cambridge [Cambridgeshire] : Cambridge University Press, 1984  x, 458 p. ; 24 cm
シリーズ名: Cambridge monographs on mathematical physics ; . Spinors and space-time ; v. 1
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目次情報: 続きを見る
Preface
The geometry of world-vectors and spin-vectors / 1：
Abstract indices and spinor algebra / 2：
Spinors and world-tensors / 3：
Differentiation and curvature / 4：
Fields in space-time / 5：
Appendix
References
Subject and author index
Index of symbols
Preface
The geometry of world-vectors and spin-vectors / 1：
Abstract indices and spinor algebra / 2：
25.

図書
図書
25. Partial differential relations (: U.S. ; : Germany ; : softcover)
Mikhael Gromov
出版情報: Berlin ; Tokyo : Springer-Verlag, c1986  ix, 363 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 9
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26.

図書
図書
26. Differential geometry, gauge theories, and gravity (: pbk)
M. Göckeler, T. Schücker
出版情報: Cambridge ; New York : Cambridge University Press, 1989  xii, 230 p. ; 23 cm
シリーズ名: Cambridge monographs on mathematical physics
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目次情報: 続きを見る
Preface
Exterior algebra / 1：
Differential forms on open subsets of Rn / 2：
Metric structures / 3：
Gauge theories / 4：
Einstein-Cartan theory / 5：
The Lie derivative / 6：
Manifolds / 7：
Lie groups / 8：
Fibre bundles / 9：
Monopoles, instantons, and related fibre bundles / 10：
Spin / 11：
An algebraic approach to anomalies / 12：
Anomalies from graphs / 13：
References
Bibliography
Notation
Index
Preface
Exterior algebra / 1：
Differential forms on open subsets of Rn / 2：
27.

図書
図書
27. Symplectic geometry and secondary characteristic classes (: us ; : gw)
Izu Vaisman
出版情報: Boston : Birkhäuser, 1987  viii, 215 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 72
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28.

図書
図書
28. Differential geometry of foliations : the fundamental integrability problem (: gw ; : us)
Bruce L. Reinhart
出版情報: Berlin ; New York : Springer-Verlag, 1983  ix, 194 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 99
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