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An introduction to differentiable manifolds and Riemannian geometry. 2nd ed. (English) Zbl 0596.53001

Pure and Applied Mathematics, 120. Orlando etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers). XVI, 430 p. hbk: $ 59.00; pbk: $ 32.95 (1986).
It is worthwile to quote the following passage from the Preface to the present edition [for the first edition (1975) see Zbl 0333.53001]: ”There are, in fact, changes on almost every second or third page, some slight and some substantial: a number of proofs have been modified or improved; the historical notes have been enlarged; and the references have been updated. It is hoped that this has improved the readability while preserving whatever good qualities were there before.”
Introduction to manifolds, functions of several variables and mappings, differentiable manifolds and submanifolds, vector fields on manifolds, tensors and tensor fields on manifolds, integration on manifolds, differentiation on Riemannian manifolds and curvature are the chapter headings. Complete proofs of Brouwer’s fixed point theorem, the Hopf- Rinow theorem and of the nonexistence of nowhere vanishing continuous vector fields on even-dimensional spheres are given. This book continues to be an excellent text on differentiable manifolds and Riemannian geometry.

MSC:

53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
58-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis

Citations:

Zbl 0333.53001