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Foundations of Differential Geometry, Volume 1 [Minkštas viršelis]

(University of California, Berkeley), (Brown University, Providence, Rhode Island)
  • Formatas: Paperback / softback, 352 pages, aukštis x plotis x storis: 224x145x25 mm, weight: 476 g
  • Serija: Wiley Classics Library
  • Išleidimo metai: 21-Mar-1996
  • Leidėjas: Wiley-Interscience
  • ISBN-10: 0471157333
  • ISBN-13: 9780471157335
Kitos knygos pagal šią temą:
Foundations of Differential Geometry, Volume 1Didesnis paveikslėlis
  • Formatas: Paperback / softback, 352 pages, aukštis x plotis x storis: 224x145x25 mm, weight: 476 g
  • Serija: Wiley Classics Library
  • Išleidimo metai: 21-Mar-1996
  • Leidėjas: Wiley-Interscience
  • ISBN-10: 0471157333
  • ISBN-13: 9780471157335
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780471157335.html
Raktažodžiai:
This 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. Volume 1 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. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.
Interdependence of the
Chapters and the Sections		 xi
Differentiable Manifolds
Differentiable manifolds
1(16)
Tensor algebras
17(9)
Tensor fields
26(12)
Lie groups
38(12)
Fibre bundles
50(13)
Theory of Connections
Connections in a principal fibre bundle
63(4)
Existence and extension of connections
67(1)
Parallelism
68(3)
Holonomy groups
71(4)
Curvature form and structure equation
75(4)
Mappings of connections
79(4)
Reduction theorem
83(6)
Holonomy theorem
89(3)
Flat connections
92(2)
Local and infinitesimal holonomy groups
94(9)
Invariant connections
103(10)
Linear and Affine Connections
Connections in a vector bundle
113(5)
Linear connections
118(7)
Affine connections
125(5)
Developments
130(2)
Curvature and torsion tensors
132(6)
Geodesics
138(2)
Expressions in local coordinate systems
140(6)
Normal coordinates
146(5)
Linear infinitesimal holonomy groups
151(3)
Riemannian Connections
Riemannian metrics
154(4)
Riemannian connections
158(4)
Normal coordinates and convex neighborhoods
162(10)
Completeness
172(7)
Holonomy groups
179(8)
The decomposition theorem of de Rham
187(6)
Affine holonomy groups
193(5)
Curvature and Space Forms
Algebraic preliminaries
198(3)
Sectional curvature
201(3)
Spaces of constant curvature
204(5)
Flat affine and Riemannian connections
209(16)
Transformations
Affine mappings and affine transformations
225(4)
Infinitesimal affine transformations
229(7)
Isometries and infinitesimal isometries
236(8)
Holonomy and infinitesimal isometries
244(4)
Ricci tensor and infinitesimal isometries
248(4)
Extension of local isomorphisms
252(4)
Equivalence problem
256(11)
Appendices
1. Ordinary linear differential equations
267(2)
2. A connected, locally compact metric space is separable
269(3)
3. Partition of unity
272(3)
4. On an arcwise connected subgroup of a Lie group
275(2)
5. Irreducible subgroups of O(n)
277(4)
6. Green's theorem
281(3)
7. Factorization lemma
284(3)
Notes
1. Connections and holonomy groups
287(4)
2. Complete affine and Riemannian connections
291(1)
3. Ricci tensor and scalar curvature
292(2)
4. Spaces of constant positive curvature
294(3)
5. Flat Riemannian manifolds
297(3)
6. Parallel displacement of curvature
300(1)
7. Symmetric spaces
300(4)
8. Linear connections with recurrent curvature
304(2)
9. The automorphism group of a geometric structure
306(2)
10. Groups of isometries and affine transformations with maximum dimensions
308(1)
11. Conformal transformations of a Riemannian manifold
309(4)
Summary of Basic Notations 313(2)
Bibliography 315(10)
Index 325(5)
Errata for Foundations of Differential Geometry, Volume I 330(1)
Errata for Foundations of Differential Geometry, Volume II 331
Shoshichi Kobayashi 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. Kobayashi's research spans the areas of differential geometry of real and complex variables, and his numerous resulting publications include several book: Foundations of Differential Geometry with K. Nomizu, Hyperbolic Complex Manifolds and Holomorphic Mappings and Differential Geometry of Complex Vector Bundles.