Overview

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, they introduce the theory of immersion of manifolds and the second fundamental form. The concluding Chapter 11 contains more complicated results on which much of the research in Riemannian geometry is based: the Morse index theorem, Synge's theorem on closed geodesics, Rauch's comparision theorem, and Bishop's volume-comparision theorem. Clear, concise writing as well as many exercises and examples make this classic an excellent text for a first-year graduate course on differential geometry.

Full Product Details

9781470484729

Table of Contents

Reviews

From a review of the First Edition: """"This book represents an excellent treatment of a wide section of modern differential geometry ... The style is elegant and at the same time considerate for the needs of a beginner ... a great number of well chosen problems with pertinent references ... anybody who chooses to base his course on differential geometry at the graduate level on this book could do no better."""" — Mathematical Reviews

Author Information

Richard L. Bishop, University of Illinois, Urbana, IL and Richard J. Crittenden

Tab Content 6

Countries Available