Description

Book Synopsis
Presents the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. This work emphasizes the geometry of Riemannian manifolds, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory.

Table of Contents
Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second fundamental form Second variation of arc length Theorems on differential equations Bibliography Subject index.

Geometry of Manifolds

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A Hardback by Richard L. Bishop, Richard J. Crittenden

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    View other formats and editions of Geometry of Manifolds by Richard L. Bishop

    Publisher: MP-AMM American Mathematical
    Publication Date: 8/30/2001 12:00:00 AM
    ISBN13: 9780821829233, 978-0821829233
    ISBN10: 0821829238
    Also in:
    Topology

    Description

    Book Synopsis
    Presents the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. This work emphasizes the geometry of Riemannian manifolds, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory.

    Table of Contents
    Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second fundamental form Second variation of arc length Theorems on differential equations Bibliography Subject index.

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