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Foundations of differential geometry: 2

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Bibliographic Details
Main Authors:	Kobayashi, Shōshichi 1932-2012 (Author), Nomizu, Katsumi 1924-2008 (Author)
Format:	Book
Language:	English
Published:	New York [u.a.] Wiley 1996
Edition:	Wiley classics library ed.
Series:	Interscience tracts in pure and applied mathematics ...
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007770005&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	XV, 468 S.
ISBN:	0471157325 9780471157328

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adam_text	CONTENTS OF VOLUME II Chapter VII Submanifolds 1. Frame bundles of a submanifold ..... 1 2. The Gauss map ........ 6 3. Covariant differentiation and second fundamental form . 10 4. Equations of Gauss and Codazzi ..... 22 5. Hypersurfaces in a Euclidean space .... 29 6. Type number and rigidity ...... 42 7. Fundamental theorem for hypersurfaces .... 47 8. Auto-parallel submanifolds and totally geodesic submani¬ folds .......... 53 Chapter VIII Variations of the Length Integral 1. Jacobi fields ........ 63 2. Jacobi fields in a Riemannian manifold .... 68 3. Conjugate points . . . . . . .71 4. Comparison theorem ....... 76 5. The first and second variations of the length integral . 79 6. Index theorem of Morse ...... 88 7. Cut loci .........96 8. Spaces of non-positive curvature . . . . .102 9. Center of gravity and fixed points of isometries . .108 Chapter IX Complex Manifolds 1. Algebraic preliminaries . . . . . .114 2. Almost complex manifolds and complex manifolds . . 121 3. Connections in almost complex manifolds . . .141 4. Hermitian metrics and Kaehler metrics . . . .146 5. Kaehler metrics in local coordinate systems . . .155 6. Examples of Kaehler manifolds . . . . .159 7. Holomorphic sectional curvature . . . . .165 8. De Rham decomposition of Kaehler manifolds . . 171 XU CONTENTS OF VOLUME II 9. Curvature of Kaehler submanifolds . . · .175 10. Hermitian connections in Hermitian vector bundles. . 178 Chapter X Homogeneous Spaces 1. Invariant affine connections . . . · · .186 2. Invariant connections on reductive homogeneous spaces . 190 3. Invariant indefinite Riemannian metrics . . · 200 4. Holonomy groups of invariant connections . . · 204 5. The de Rham decomposition and irreducibility . .210 6. Invariant almost complex structures . . . .216 Chapter XI Symmetric Spaces 1. Affine locally symmetric spaces ..... ^ 2. Symmetric spaces ......·· 225 3. The canonical connection on a symmetric space . · 230 4. Totally geodesic submanifolds . . . . · 234 5. Structure of symmetric Lie algebras . 238 6. Riemannian symmetric spaces ..... 24j 7. Structure of orthogonal symmetric Lie algebras . · 246 8. Duality ......... 253 9. Hermitian symmetric spaces ...... 259 10. Examples ......... 264 11. An outline of the classification theory .... 289 Chapter XII Characteristic Glasees 1. Weil homomorphism ....... 293 2. Invariant polynomials ....... 298 3. Chem classes ........ 305 4. Pontrjagin classes ....... 312 5. Euler classes .... ... 314 Appendices 8. Integrable real analytic almost complex structures . .321 9. Some definitions and fects on Lie algebras . . .325 CONTENTS OF VOLUME II Xlii Notes 12. Connections and holonomy groups (Supplement to Note 1) 331 13. The automorphism group of a geometric structure (Supple¬ ment to Note 9)........ 332 14. The Laplacian ........ 337 15. Surfaces of constant curvature in R3 . . . 343 16. Index of nullity ........ 347 17. Type number and rigidity of imbedding . . . 349 18. Isometric imbeddings ....... 354 19. Equivalence problems for Riemannian manifolds . . 357 20. Gauss-Bonnet theorem ....... 358 21. Total curvature ........ 361 22. Topology of Riemannian manifolds with positive curvature 364 23. Topology of Kaehler manifolds with positive curvature . 368 24. Structure theorems on homogeneous complex manifolds . 373 25. Invariant connections on homogeneous spaces . . .375 26. Complex submanifolds ....... 378 27. Minimal submanifolds ....... 379 28. Contact structure and related structures . . .381 Bibliography ........ 387 Summary of Basic Notations ...... 455 Index for Volumes I and II . . . . . 459 Errata for Foundations of Differential Geometry, Volume I . 469 Errata for Foundations of Differential Geometry, Volume II . 470
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spellingShingle	Kobayashi, Shōshichi 1932-2012 Nomizu, Katsumi 1924-2008 Foundations of differential geometry
title	Foundations of differential geometry
title_auth	Foundations of differential geometry
title_exact_search	Foundations of differential geometry
title_full	Foundations of differential geometry 2 Shoshichi Kobayashi and Katsumi Nomizu
title_fullStr	Foundations of differential geometry 2 Shoshichi Kobayashi and Katsumi Nomizu
title_full_unstemmed	Foundations of differential geometry 2 Shoshichi Kobayashi and Katsumi Nomizu
title_short	Foundations of differential geometry
title_sort	foundations of differential geometry
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Call Number:	0302 MAT 530f 1996 A 8722-2 Floor plan
Copy 1	Available for loan On Shelf