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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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国外数学名著系列（续一）（影印版）60：几何Ⅵ黎曼几何

最 低 价：￥66.20

定 价：￥96.00

作 者：（俄罗斯）波斯特尼科夫 著 著

出 版 社：科学出版社

出版时间：2009-1-1

I S B N：9787030235039

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    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.

    作者简介

    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

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