An Introduction to Differentiable Manifolds and Riemannian Geometry

The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by “beginners” in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields.

Table of Contents

I. Introduction to Manifolds

II. Functions of Several Variables and Mappings

III. Differentiable Manifolds and Submanifolds

IV. Vector Fields on a Manifold

V. Tensors and Tensor Fields on Manifolds

VI. Integration on Manifolds

VII. Differentiation on Riemannian Manifolds

VIII. Curvature

About the Author

William Boothby received his Ph.D. at the University of Michigan and was a professor of mathematics for over 40 years. In addition to teaching at Washington University, he taught courses in subjects related to this text at the University of Cordoba (Argentina), the University of Strasbourg (France), and the University of Perugia (Italy).