{"product_id":"foundations-of-differential-geometry-2-volume-set-isbn-9780470555583","title":"Foundations of Differential Geometry, 2 Volume Set","description":"\u003cb\u003eThis set features:\u003c\/b\u003e \u003cp\u003e\u003ci\u003eFoundations of Differential Geometry, Volume 1\u003c\/i\u003e (978-0-471-15733-5) and \u003ci\u003eFoundations of Differential Geometry, Volume 2\u003c\/i\u003e (978-0-471-15732-8), both by Shoshichi Kobayashi and Katsumi Nomizu\u003c\/p\u003e \u003cp\u003eThis two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. \u003cb\u003eVolume 1\u003c\/b\u003e presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. \u003cb\u003eVolume 2\u003c\/b\u003e continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.\u003c\/p\u003e \u003cp\u003eVOLUME I\u003c\/p\u003e \u003cp\u003eInterdependence of the Chapters and the Sections xi\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter I\u003c\/p\u003e \u003cp\u003eDifferentiable Manifolds\u003c\/p\u003e \u003cp\u003e1. Differentiable manifolds 1\u003c\/p\u003e \u003cp\u003e2. Tensor algebras 17\u003c\/p\u003e \u003cp\u003e3. Tensor fields 26\u003c\/p\u003e \u003cp\u003e4. Lie groups 38\u003c\/p\u003e \u003cp\u003e5. Fibre bundles 50\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter II\u003c\/p\u003e \u003cp\u003eTheory of Connections\u003c\/p\u003e \u003cp\u003e1. Connections in a principle fibre bundle 63\u003c\/p\u003e \u003cp\u003e2. Existence and extension of connections 67\u003c\/p\u003e \u003cp\u003e3. Parallelism 68\u003c\/p\u003e \u003cp\u003e4. Holonomy groups 71\u003c\/p\u003e \u003cp\u003e5. Curvature for and structure equation 75\u003c\/p\u003e \u003cp\u003e6. Mappings of connections 79\u003c\/p\u003e \u003cp\u003e7. Reduction theorem 83\u003c\/p\u003e \u003cp\u003e8. Holonomy theorem 89\u003c\/p\u003e \u003cp\u003e9. Flat connections 92\u003c\/p\u003e \u003cp\u003e10. Local and infinitesimal holonomy groups 94\u003c\/p\u003e \u003cp\u003e11. Invariant connections 103\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter III\u003c\/p\u003e \u003cp\u003eLinear and Affine Connections\u003c\/p\u003e \u003cp\u003e1. Connections in a vector bundle 113\u003c\/p\u003e \u003cp\u003e2. Linear connections 118\u003c\/p\u003e \u003cp\u003e3. Affine connections 125\u003c\/p\u003e \u003cp\u003e4. Developments 130\u003c\/p\u003e \u003cp\u003e5. Curvature and torsion tensors 132\u003c\/p\u003e \u003cp\u003e6. Geodesics 138\u003c\/p\u003e \u003cp\u003e7. Expressions in local coordinate systems 140\u003c\/p\u003e \u003cp\u003e8. Normal coordinates 146\u003c\/p\u003e \u003cp\u003e9. Linear infitesimal holonomy groups 151\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter IV\u003c\/p\u003e \u003cp\u003eRiemannian Connections\u003c\/p\u003e \u003cp\u003e1. Riemannian metrics 154\u003c\/p\u003e \u003cp\u003e2. Riemannian connections 158\u003c\/p\u003e \u003cp\u003e3. Normal coordinates and convex neighborhoods 162\u003c\/p\u003e \u003cp\u003e4. Completeness 172\u003c\/p\u003e \u003cp\u003e5. Holonomy groups 179\u003c\/p\u003e \u003cp\u003e6. The decomposition theorem of de Rham 187\u003c\/p\u003e \u003cp\u003e7. Affine holonomy groups\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter V\u003c\/p\u003e \u003cp\u003eCurvature and Space Forms\u003c\/p\u003e \u003cp\u003e1. Algebraic preliminaries 198\u003c\/p\u003e \u003cp\u003e2. Sectional curvature\u003c\/p\u003e \u003cp\u003e3. Spaces of constant curvature 204\u003c\/p\u003e \u003cp\u003e4. Flat affine and Riemannian connections 209\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter VI\u003c\/p\u003e \u003cp\u003eTransformations\u003c\/p\u003e \u003cp\u003e1. Affine mappings and affine transformations 225\u003c\/p\u003e \u003cp\u003e2. Infinitesimal affine transformations 229\u003c\/p\u003e \u003cp\u003e3. Isometries and infinitesimal isometries 236\u003c\/p\u003e \u003cp\u003e4. Holonomy and infinitesimal isometries 244\u003c\/p\u003e \u003cp\u003e5. Ricci tensor and infinitesimal isometries 248\u003c\/p\u003e \u003cp\u003e6. Extension of local isomorphisms 252\u003c\/p\u003e \u003cp\u003e7. Equivalence problem 256\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eAppendices\u003c\/p\u003e \u003cp\u003e1. Ordinary linear differential equations 267\u003c\/p\u003e \u003cp\u003e2. A connected, locally compact metric space is separable 269\u003c\/p\u003e \u003cp\u003e3. Partition of unity 272\u003c\/p\u003e \u003cp\u003e4. On an arcwise connected subgroup of a Lie group 275\u003c\/p\u003e \u003cp\u003e5. Irreducible subgroups of O(n) 277\u003c\/p\u003e \u003cp\u003e6. Green's theorem 281\u003c\/p\u003e \u003cp\u003e7. Factorization lemma 284\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eNotes\u003c\/p\u003e \u003cp\u003e1. Connections and holonomy groups 287\u003c\/p\u003e \u003cp\u003e2. Complete affine and Riemannian connections 291\u003c\/p\u003e \u003cp\u003e3. Ricci tensor and scalar curvature 292\u003c\/p\u003e \u003cp\u003e4. Spaces of constant positive curvature 294\u003c\/p\u003e \u003cp\u003e5. Flat Riemannian manifolds 297\u003c\/p\u003e \u003cp\u003e6. Parallel displacement of curvature 300\u003c\/p\u003e \u003cp\u003e7. Symmetric spaces 300\u003c\/p\u003e \u003cp\u003e8. Linear connections with recurrent curvature 304\u003c\/p\u003e \u003cp\u003e9. The automorphism group of a geometric structure 306\u003c\/p\u003e \u003cp\u003e10. Groups of isometries and affine transformations with maximum dimensions 308\u003c\/p\u003e \u003cp\u003e11. Conformal transformations of a Riemannian manifold 309\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eSummary of Basic Notations 313\u003c\/p\u003e \u003cp\u003eBibliography 315\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eIndex 325\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eErrata for Foundations of Differential Geometry, Volume I 330\u003c\/p\u003e \u003cp\u003eErrata for Foundations of Differential Geometry, Volume II 331\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e \u003cp\u003eVOLUME II\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter VII\u003c\/p\u003e \u003cp\u003eSubmanifolds\u003c\/p\u003e \u003cp\u003e1. Frame bundles of a submanifold 1\u003c\/p\u003e \u003cp\u003e2. The Gauss map 6\u003c\/p\u003e \u003cp\u003e3. Covariant differentiation and second fundamental form 10\u003c\/p\u003e \u003cp\u003e4. Equations of Gauss and Codazzi 22\u003c\/p\u003e \u003cp\u003e5. Hypersurfaces in a Euclidean space 29\u003c\/p\u003e \u003cp\u003e6. Type number and rigidity 42\u003c\/p\u003e \u003cp\u003e7. Fundamental theorem for hypersurfaces 47\u003c\/p\u003e \u003cp\u003e8. Auto-parallel submanifolds and totally geodesic submanifolds 53\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter VIII\u003c\/p\u003e \u003cp\u003eVariations of the Length Integral\u003c\/p\u003e \u003cp\u003e1. Jacobi fields 63\u003c\/p\u003e \u003cp\u003e2. Jacobi fields in a Rimannian manifold 68\u003c\/p\u003e \u003cp\u003e3. Conjugate points 71\u003c\/p\u003e \u003cp\u003e4. Comparison theorem 76\u003c\/p\u003e \u003cp\u003e5. The first and second variations of the length integral 79\u003c\/p\u003e \u003cp\u003e6. Index theorem of Morse 88\u003c\/p\u003e \u003cp\u003e7. Cut loci 96\u003c\/p\u003e \u003cp\u003e8. Spaces of non-positive curvature 102\u003c\/p\u003e \u003cp\u003e9. Center of gravity and fixed points of isometries 108\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter IX\u003c\/p\u003e \u003cp\u003eComplex Manifolds\u003c\/p\u003e \u003cp\u003e1. Algebraic preliminaries 114\u003c\/p\u003e \u003cp\u003e2. Almost complex manifolds and complex manifolds 121\u003c\/p\u003e \u003cp\u003e3. Connections in almost complex manifolds 141\u003c\/p\u003e \u003cp\u003e4. Hermitian metrics and Kaehler metrics 146\u003c\/p\u003e \u003cp\u003e5. Kaehler metrics in local coordinate systems 155\u003c\/p\u003e \u003cp\u003e6. Examples of Kaehler manifolds 159\u003c\/p\u003e \u003cp\u003e7. Holomorphic sectional curvature 165\u003c\/p\u003e \u003cp\u003e8. De Rham decomposition of Kaehler manifolds 171\u003c\/p\u003e \u003cp\u003e9. Curvature of Kaehler submanifolds 175\u003c\/p\u003e \u003cp\u003e10. Hermitian connections in Hermitian vector bundles 178\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter X\u003c\/p\u003e \u003cp\u003eHomogeneous Spaces\u003c\/p\u003e \u003cp\u003e1. Invariant affine connections 186\u003c\/p\u003e \u003cp\u003e2. Invariant connections on reductive homogeneous spaces 190\u003c\/p\u003e \u003cp\u003e3. Invariant indefinite Riemannian metrics 200\u003c\/p\u003e \u003cp\u003e4. Holonomy groups of invariant connections 204\u003c\/p\u003e \u003cp\u003e5. The de Rham decomposition and irreducibility 210\u003c\/p\u003e \u003cp\u003e6. Invariant almost complex structures 216\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter XI\u003c\/p\u003e \u003cp\u003eSymmetric Spaces\u003c\/p\u003e \u003cp\u003e1. Affine locally symmetric spaces 222\u003c\/p\u003e \u003cp\u003e2. Symmetric spaces 225\u003c\/p\u003e \u003cp\u003e3. The canonical connection on symmetric space 230\u003c\/p\u003e \u003cp\u003e4. Totally geodesic submanifolds 234\u003c\/p\u003e \u003cp\u003e5. Structure of symmetric Lie algebras 238\u003c\/p\u003e \u003cp\u003e6. Riemannian symmetric spaces 243\u003c\/p\u003e \u003cp\u003e7. Structure of orthogonal symmetric Lie algebras 246\u003c\/p\u003e \u003cp\u003e8. Duality 253\u003c\/p\u003e \u003cp\u003e9. Hermitian symmetric spaces 259\u003c\/p\u003e \u003cp\u003e10. Examples 264\u003c\/p\u003e \u003cp\u003e11. An outline of the classification theory\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eChapter XII\u003c\/p\u003e \u003cp\u003eCharacteristic Classes\u003c\/p\u003e \u003cp\u003e1. Weil homomorphism 293\u003c\/p\u003e \u003cp\u003e2. Invaraint polynomials 298\u003c\/p\u003e \u003cp\u003e3. Chern classes 305\u003c\/p\u003e \u003cp\u003e4. Pontrjagin classes 312\u003c\/p\u003e \u003cp\u003e5. Euler classes 314\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eAppendices\u003c\/p\u003e \u003cp\u003e8. Integrable real analytic almost complex structures 321\u003c\/p\u003e \u003cp\u003e9. Some definitions and facts on Lie algebras 325\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eNotes\u003c\/p\u003e \u003cp\u003e12. Connections and holonomy groups (Supplement to Note 1) 331\u003c\/p\u003e \u003cp\u003e13. The automorphism group of geometric structure (Supplement to Note 9) 332\u003c\/p\u003e \u003cp\u003e14. The Laplacian 337\u003c\/p\u003e \u003cp\u003e15. Surafces of constant curvature in R3 343\u003c\/p\u003e \u003cp\u003e16. Index of nullity 347\u003c\/p\u003e \u003cp\u003e17. Type number and rigidity of imbedding 349\u003c\/p\u003e \u003cp\u003e18. Isometric imbeddings 354\u003c\/p\u003e \u003cp\u003e19. Equivalence problems for Riemannian manifolds 357\u003c\/p\u003e \u003cp\u003e20. Gauss-Bonnet theorem 358\u003c\/p\u003e \u003cp\u003e21. Total curvature 361\u003c\/p\u003e \u003cp\u003e22. Topology of Riemannian manifolds with positive curvature 364\u003c\/p\u003e \u003cp\u003e23. Topology of Kaehler manifolds with positive curvature 368\u003c\/p\u003e \u003cp\u003e24. Structure theorems on homogeneous complex manifols 373\u003c\/p\u003e \u003cp\u003e25. Invariant connections on homogeneous spaces 375\u003c\/p\u003e \u003cp\u003e26. Complex submanifolds 378\u003c\/p\u003e \u003cp\u003e27. Minimal submanifolds 379\u003c\/p\u003e \u003cp\u003e28. Contact structure and related structures 381\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eBibliography 387\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eSummary of Basic Notations 455\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eIndex for Volumes I and II 459\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eErrata for Foundations of Differential Geometry, Volume I 469\u003c\/p\u003e \u003cp\u003eErrata for Foundations of Differential Geometry, Volume II 470\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003eShoshichi Kobayashi\u003c\/b\u003e was born January 4, 1932 in Kofu, Japan. After obtaining his mathematics degree from the University of Tokyo and his Ph.D. from the University of Washington, Seattle, he held positions at the Institute for Advanced Study, Princeton, at MIT and at the University of British Columbia between 1956 and 1962, and then moved to the University of California, Berkeley, where he is now Professor in the Graduate School.\u003cbr\u003eKobayashi's research spans the areas of differential geometry of real and complex variables, and his numerous resulting publications include several book: \u003ci\u003eFoundations of Differential Geometry\u003c\/i\u003e with \u003cb\u003eK. Nomizu\u003c\/b\u003e, \u003ci\u003eHyperbolic Complex Manifolds and Holomorphic Mappings\u003c\/i\u003e and \u003ci\u003eDifferential Geometry of Complex Vector Bundles\u003c\/i\u003e.","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989237874917,"sku":"NP9780470555583","price":299.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470555583.jpg?v=1761783327","url":"https:\/\/k12savings.com\/products\/foundations-of-differential-geometry-2-volume-set-isbn-9780470555583","provider":"K12savings","version":"1.0","type":"link"}