国外数学名著系列（续一）（影印版）60：几何Ⅵ黎曼几何
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作者： （俄罗斯）波斯特尼科夫 著
出 版 社： 科学出版社
出版时间： 2009-1-1字数： 634000版次： 1页数： 503印刷时间： 2009/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9787030235039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.
The results are well presented and useful for students in mathematics and theoretical physics，and for experts in these fields.The book can serve as a textbook for students doing geometry，as well as a reference book for professional mathematicians and physicists.
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
Chapter 30.Smooth Manifolds
Chapter 31.Tangent Vectors
Chapter 32.Submanifolds of a Smooth Manifold
Chapter 33.Vector and Tensor Fields Differential Forms
Chapter 34.Vector Bundles
Chapter 35.Connections on Vector Bundles
Chapter 36.Curvature Tensor
Suggested Reading
Index
