Geometry of Manifolds

2001/08/28 by Richard L. Bishop, Richard J. Crittenden · 7 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.1090/chel/344

openalex publication_date 2001/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

First published in 1964, this book served as a text on differential geometry to several generations of graduate students all over the world. The first half of the book (Chapters 1-6) presents basics of the theory of manifolds, vector bundles, differential forms, and Lie groups, with a special emphasis on the theory of linear and affine connections. The second half of the book (Chapters 7-11) is devoted to Riemannian geometry. Following the definition and main properties of Riemannian manifolds, the authors discuss the theory of geodesics, complete Riemannian manifolds, and curvature. Next, the

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