Geometry vi : riemannian geometry几何VI
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作者： M.M. Postnikov著
出 版 社： 湖南文艺出版社
出版时间： 2001-4-1字数：版次： 1页数： 503印刷时间： 2001/04/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540411086包装： 精装内容简介
This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. Before going to Riemannian geometry, the author presents a more general theory of manifolds with a linear connection. Having in mind different generalizations of Riemannian manifolds, it is clearly stressed which notions and theorems belong to Riemannian geometry and which of them are of a more general nature. Much attention is paid to transformation groups of smooth manifolds. Throughout the book, different aspects of symmetric spaces are treated. The author successfully combines the co-ordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject. The book contains a very useful large Appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources.
目录
Preface
Chapter. 1 Affine Connections
Chapter. 2 Covariant Differentiation. Curvature
Chapter. 3 Affine Mappings. Submanifolds
Chapter. 4 Structural Equations. Local Symmetries
Chapter. 5 Symmetric Spaces
Chapter. 6 Connections on Lie Groups
Chapter. 7 Lie Functor
Chapter. 8 Affine Fields and Related Topics
Chapter. 9 Cartan Theorem
Chapter. 10 Palais and Kobayashi Theorems
Chapter. 11 Lagrangians in Riemannian Spaces
Chapter. 12 Metric Properties of Geodesics
Chapter. 13 Harmonic Functionals and Related Topics
Chapter. 14 Minimal Surfaces
Chapter. 15 Curvature in Riemannian Space
Chapter. 16 Gaussian Curvature
Chapter. 17 Some Special Tensors
Chapter. 18 Surfaces with Conformal Structure
Chapter. 19 Mappings and Submanifolds I
Chapter. 20 Submanifolds II
Chapter. 21 Fundamental Forms of a Hypersurface
Chapter. 22 Spaces of Constant Curvature
Chapter. 23 Space Forms
Chapter. 24 Four-Dimensional Manifolds
Chapter. 25 Metrics on a Lie Group I
Chapter. 26 Metrics on a Lie Group II
Chapter. 27 Jacobi theory
Chapter. 28 Some Additional Theorems I
Chapter. 29 Some Additional Theorems II
Addendum
Chapter. 30 Smooth Manifolds
Chapter. 31 Tangent Vectors
Chapter. 32 Submanifolds of a Smooth Manifold
Chapter. 33 Vector and Tensor Fields. Differential Forms
Chapter. 34Vector Bundles
Chapter. 35 Connections on Vector Bundle
Chapter. 36 Curvature Tensor
Suggested reading
Index
