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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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