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Foundations of Differential Geometry, Volume 1

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Foundations of Differential Geometry, Volume 1

Shoshichi Kobayashi, Katsumi Nomizu

ISBN: 978-0-471-15733-5 February 1996 344 Pages

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This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

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Differentiable Manifolds.

Theory of Connections.

Linear and Affine Connections.

Riemannian Connections.

Curvature and Space Forms.

Transformations.

Appendices.

Notes.

Summary of Basic Notations.

Bibliography.

Index.