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1.

図書
図書
1. Differential geometry : bundles, connections, metrics and curvature (: hbk ; : pbk)
Clifford Henry Taubes
出版情報: New York ; Oxford : Oxford University Press, 2011  xiii, 298 p. ; 24 cm
シリーズ名: Oxford graduate texts in mathematics ; 23
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2.

図書
図書
2. Geometrical properties of differential equations : applications of the Lie group analysis in financial mathematics
Ljudmila A. Bordag
出版情報: New Jersey : World Scientific, c2015  xi, 328 p. ; 24 cm
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3.

図書
図書
3. Differential geometry : curves - surfaces - manifolds. 3rd ed
Wolfgang Kühnel ; translated by Bruce Hunt
出版情報: Providence, R.I. : American Mathematical Society, c2015  xii, 402 p. ; 22 cm
シリーズ名: Student mathematical library ; v. 77
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4.

図書
図書
4. Applications of differential geometry to econometrics (: pbk.)
edited by Paul Marriott and Mark Salmon
出版情報: Cambridge : Cambridge University Press, 2010  viii, 324 p. ; 23 cm
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目次情報: 続きを見る
Introduction / P. Marriott ; M. Salmon
An introduction to differential geometry / 1：
Orthogonal projection, nested models and encompassing / Maozu Lu ; G. Mizon2：
Exact properties of the maximum likelihood estimator in exponential regression models / G. Hillier ; R. O'Brien3：
Empirical likelihood estimation and inference / R. Smith4：
Measuring earnings differentials with frontier functions and Rao distances / U. Jensen5：
First order predictive densities / J. M. Corcuera ; F. Giummole6：
An alternative comparison of classical tests: assessing the effects of curvature / K. J. van Garderen7：
Testing for unit roots in AR and MA Models / T. Rothenberg8：
Efficiency and robustness in a geometrical perspective / R. Davidson9：
Paramaterisations and transformations; An elementary introduction to Amari's differential geometry / F. Critchley10：
Introduction / P. Marriott ; M. Salmon
An introduction to differential geometry / 1：
Orthogonal projection, nested models and encompassing / Maozu Lu ; G. Mizon2：
5.

図書
図書
5. Geometry from a differentiable viewpoint. 2nd ed (: hbk ; : pbk)
John McCleary
出版情報: Cambridge [England] ; New York : Cambridge University Press, 2013  xv, 357 p. ; 26 cm
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目次情報: 続きを見る
Prelude and Themes: Synthetic Methods and Results: / Part I：
Spherical geometry / 1：
Euclid / 2：
The theory of parallels / 3：
Non-Euclidean geometry / 4：
Development: Differential Geometry: / Part II：
Curves in the plane / 5：
Curves in space / 6：
Surfaces / 7：
Curvature for surfaces / 8：
Metric equivalence of surfaces / 9：
Geodesics / 10：
The Gauss-Bonnet theorem / 11：
Constant-curvature surfaces / 12：
Recapitulation and Coda: / Part III：
Abstract surfaces / 13：
Modeling the non-Euclidean plane / 14：
Epilogue: where from here? / 15：
Prelude and Themes: Synthetic Methods and Results: / Part I：
Spherical geometry / 1：
Euclid / 2：
6.

図書
図書
6. Jordan structures in geometry and analysis
Cho-Ho Chu
出版情報: Cambridge, UK ; Tokyo : Cambridge University Press, 2012  x, 261 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 190
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目次情報: 続きを見る
Preface
Jordan and Lie theory / 1：
Jordan algebras / 1.1：
Jordan triple systems / 1.2：
Lie algebras and the Tits-Kantor-Koecher construction / 1.3：
Matrix Lie groups / 1.4：
Notes
Jordan structures in geometry / 2：
Banach manifolds and Lie groups / 2.1：
Riemannian manifolds / 2.2：
Jordan algebras and Riemannian symmetric spaces / 2.3：
Jordan triples and Riemannian symmetric spaces / 2.4：
Jordan triples and symmetric domains / 2.5：
Jordan structures in analysis / 3：
Banach spaces / 3.1：
Holomorphic mappings / 3.2：
Contractive projections on JB*-triples / 3.3：
Isometries between JB-triples / 3.4：
Hilbert spaces / 3.5：
Bibliography
Index
Preface
Jordan and Lie theory / 1：
Jordan algebras / 1.1：
7.

図書
図書
7. Harmonic vector fields : variational principles and differential geometry
Sorin Dragomir, Domenico Perrone
出版情報: Amsterdam : Elsevier, c2012  xiv, 508 p. ; 24 cm
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目次情報: 続きを見る
Preface
Geometry of the Tangent Bundle / 1：
The Tangent Bundle / 1.1：
Connections and Horizontal Vector Fields / 1.2：
The Dombrowski Map and the Sasaki Metric / 1.3：
The Tangent Sphere Bundle / 1.4：
The Tangent Sphere Bundle over a Torus / 1.5：
Harmonic Vector Fields / 2：
Vector Fields as Isometric Immersions / 2.1：
The Energy of a Vector Field / 2.2：
Vector Fields Which Are Harmonic Maps / 2.3：
The Tension of a Vector Field / 2.4：
Variations through Vector Fields / 2.5：
Unit Vector Fields / 2.6：
The Second Variation of the Energy Function / 2.7：
Unboundedness of the Energy Functional / 2.8：
The Dirichlet Problem / 2.9：
Conformal Change of Metric on the Torus / 2.10：
Sobolev Spaces of Vector Fields / 2.11：
Harmonicity and Stability / 3：
Hopf Vector Fields on Spheres / 3.1：
The Energy of Unit Killing Fields in Dimension 3 / 3.2：
instability of Hopf Vector Fields / 3.3：
Existence of Minima in Dimension > 3 / 3.4：
Brito's Functional / 3.5：
The Brito Energy of the Reeb Vector / 3.6：
Vector Fields with Singularities / 3.7：
Normal Vector Fields on Principal Orbits / 3.8：
RiemannianTori / 3.9：
Harmonicity and Contact Metric Structures / 4：
H-Contact Manifolds / 4.1：
Three-Dimensional H-Contact Manifolds / 4.2：
Stability of the Reeb Vector Field / 4.3：
Harmonic Almost Contact Structures / 4.4：
Reeb Vector Fields on Real Hypersurfaces / 4.5：
Harmonicity and Stability of the Geodesic Flow / 4.6：
Harmonicity with Respect to g-Natural Metrics / 5：
g-Natural Metrics / 5.1：
Naturally Harmonic Vector Fields / 5.2：
Vector Fields Which Are Naturally Harmonic Maps / 5.3：
Geodesic Flow with Respect to g-Natural Metrics / 5.4：
The Energy of Sections / 6：
The Horizontal Bundle / 6.1：
The Sasaki Metric / 6.2：
The Sphere Bundle U(E) / 6.3：
The Energy of Cross Sections / 6.4：
Unit Sections / 6.5：
Harmonic Sections in Normal Bundles / 6.6：
The Energy of Oriented Distributions / 6.7：
Examples of Harmonic Distributions / 6.8：
The Chacon-Naveira Energy / 6.9：
Harmonic Vector Fields in CR Geometry / 7：
The Canonical Metric / 7.1：
Bundles of Hyperquadrics in (T(M),J, Gs) / 7.2：
Harmonic Vector Fields from C(M) / 7.3：
Boundary Values of Bergman-Harmonic Maps / 7.4：
Pseudo harmonic Maps / 7.5：
The Pseudo hermitian Biegung / 7.6：
The Second Variation Formula / 7.7：
Lorentz Geometry and Harmonic Vector Fields / 8：
A Few Notions of Lorentz Geometry / 8.1：
Energy Functionals and Tension Fields / 8.2：
The Spacelike Energy / 8.3：
The Second Variation of the Spacelike Energy / 8.4：
Conformal Vector Fields / 8.5：
Twisted Cohomologies / Appendix A：
The Stokes Theorem on Complete Manifolds / Appendix B：
Complex Monge-Ampere Equations / Appendix C：
Introduction / C.1：
Strictly Parabolic Manifolds / C.2：
Foliations and Monge-Ampere Equations / C.3：
Adapted Complex Structures / C.4：
CR Submanifolds of Grauert Tubes / C.5：
Exceptional Orbits of Highest Dimension / Appendix D：
Reilly's Formula / Appendix E：
References
Index
Preface
Geometry of the Tangent Bundle / 1：
The Tangent Bundle / 1.1：
8.

図書
図書
8. Geometric formulation of classical and quantum mechanics
Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily
出版情報: Singapore : World Scientific, c2011  xi, 392 p. ; 24 cm
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9.

図書
図書
9. Synthetic geometry of manifolds
Anders Kock
出版情報: Cambridge : Cambridge University Press, 2010  xiii, 302 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 180
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目次情報: 続きを見る
Preface
Acknowledgements
Calculus and linear algebra / 1：
The number line R / 1.1：
The basic infinitesimal spaces / 1.2：
The KL axiom scheme / 1.3：
Calculus / 1.4：
Affine combinations of mutual neighbour points / 1.5：
Geometry of the neighbour relation / 2：
Manifolds / 2.1：
Framings and 1-forms / 2.2：
Affine connections / 2.3：
Affine connections from framings / 2.4：
Bundle connections / 2.5：
Geometric distributions / 2.6：
Jets and jet bundles / 2.7：
Infinitesimal simplicial and cubical complex of a manifold / 2.8：
Combinatorial differential forms / 3：
Simplicial, whisker, and cubical forms / 3.1：
Coboundary/exteripr derivative / 3.2：
Integration of forms / 3.3：
Uniqueness of observables / 3.4：
Wedge/cup product / 3.5：
Involutive-distnbutions and differential forms / 3.6：
Non-abelian theory of 1-forms / 3.7：
Differential forms with values in a vector bundle / 3.8：
Crossed modules and non-abelian 2-forms / 3.9：
The tangent bundle / 4：
Tangent vectors and vector fields / 4.1：
Addition of tangent vectors / 4.2：
The log-exp bijection / 4.3：
Tangent vectors as differential operators / 4.4：
Cotangents, and the cotangent bundle / 4.5：
The differential operator of a linear connection / 4.6：
Classical differential forms / 4.7：
Differential forms with values in TM?M / 4.8：
Lie bracket of vector fields / 4.9：
Further aspects of the tangent bundle / 4.10：
Groupoids / 5：
Connections in groupoids / 5.1：
Actions of groupoids on bundles / 5.3：
Lie derivative / 5.4：
Deplacements in groupoids / 5.5：
Principal bundles / 5.6：
Principal connections / 5.7：
Holonomy of connections / 5.8：
Lie theory; non-abelian covariant derivative / 6：
Associative algebras / 6.1：
Differential forms with values in groups / 6.2：
Differential forms with values in a group bundle / 6.3：
Bianchi identity in terms of covariant derivative / 6.4：
Semidirecl products; covariant derivative as curvature / 6.5：
The Lie algebra of G / 6.6：
Group-valued vs. Lie-algebra-valued forms / 6.7：
Left-invariant distributions / 6.8：
Examples of enveloping algebras and enveloping algebra bundles / 6.10：
Jets and differential operators / 7：
Linear differential operators and their symbols / 7.1：
Linear deplacements as differential operators / 7.2：
Bundle-theoretic differential operators / 7.3：
Sheaf-theoretic differential operators / 7.4：
Metric notions / 8：
Pseudo-Riemannian metrics / 8.1：
Geometry of symmetric affine connections / 8.2：
Laplacian (or isotropic) neighbours / 8.3：
The Laplace operator / 8.4：
Appendix
Category theory / A.1：
Models; sheaf semantics / A.2：
A simple topos model / A.3：
Microlinearity / A.4：
Linear algebra over local rings; Grassmannians / A.5：
Topology / A.6：
Polynomial maps / A.7：
The complex of singular cubes / A.8：
"Nullstellensatz" in multilinear algebra / A.9：
Bibliography
Index
Preface
Acknowledgements
Calculus and linear algebra / 1：
10.

電子ブック
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10. Differential geometry : bundles, connections, metrics and curvature ((ebook) :)
Clifford Henry Taubes
出版情報: Oxford : Oxford University Press, 2011  1 online resource (xiii, 298 p.)
シリーズ名: Oxford graduate texts in mathematics ; 23
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