几何VI-黎曼几何 本书特色

This book treats that part of Riemanniageometry related to more classical topics ia very original， clear and solid style. Before going to Riemanniageometry， the author presents a more general theory of manifolds with a linear connection. Having imind different generalizations of Riemanniamanifolds， it is clearly stressed which notions and theorems belong to Riemanniageometry and which of them are of a more general nature. Much attentiois paid to
　　transformatiogroups 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 usefullarge appendix ofoundations of differentiable manifolds and basic structures othem which makes it self contained and practically independent from other sources.
　　The results are well presented and useful for students imathematics and theoretical physics， and for experts ithese fields.The book caserve as a textbook for students doing geometry， as well as a reference book for professional mathematicians and physicists.

几何VI-黎曼几何 内容简介

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几何VI-黎曼几何 目录

Preface
Chapter 1．Afne Connections
1．Connectiooa Manifold
2．Covariant Differentiatioand Parallel TranslatioAlong a Curve
3．Geodesics
4．Exponential Mapping and Normal Neighborhoods
5．Whitehead Theorem
6．Normal Convex Neighborhoods
7．Existence of Leray Coverings

Chapter 2．Covariant Differentiation．Curvature
1．Covariant Differentiation
2．The Case of Tensors of Type
3．TorsioTensor and Symmetric Connections
4．Geometric Meaning of the Symmetry of a Connection
5．Commutativity of Second Covariant Derivatives
6．Curvature Tensor of aAfne Connection
7．Space with Absolute Parallelism
8．Bianci Identities
9．Trace of the Curvature Tensor
10．Ricci Tensor

Chapter 3．Affine Mappings．Submanifolds
1．Afne Mappings
2．Affinities
3．Afne Coverings
4．Restrictioof a Connectioto a Submanifold
5．Induced Connectiooa Normalized Submanifold
6．Gauss Formula and the Second Fundamental Form of a Normalized Submanifold
7．Totally Geodesic and Auto—Parallel Submanifolds
8．Normal Connectioand the WeingarteFormula
9．Vader Waerden—Bortolotti Connection

Chapter 4．Structural Equations．Local Symmetries
1．Torsioand Curvature Forms
2．CaftaStructural Equations iPolar Coordinates
3．Existence of Afne Local Mappings
4．Locally Symmetric Afne ConnectioSpaces
5．Local Geodesic Symmetries
6．Semisymmetric Spaces

Chapter 5．Symmetric Spaces
1．Globally Symmetric Spaces
2．Germs of Smooth Mappings
3．Extensions of Affine Mappings
4．Uniqueness Theorem
5．Reductioof Locally Symmetric Spaces to Globally Symmetric Spaces
6．Properties of Symmetries iGlobally Symmetric Spaces
7．Symmetric Spaces
8．Examples of Symmetric Spaces
9．Coincidence of Classes of Symmetric and Globally Symmetric Spaces

Chapter 6．Connections oLie Groups
1．Invariant Constructioof the Canonical Connection
2．Morphisms of Symmetric Spaces as Affine Mappings

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自然科学 数学 几何与拓扑

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