An Introduction to Sifferentiable Manifolds and Riemannian Geometry

This book was planned and written as a text for a two-semester course designed, it is hoped, to overcome, or at least to minimize, some of these difficulties. It has, in fact, been used successfully several times in preliminary form as class notes for a two-semester course intended to lead the student from a reasonable mastery of advanced (multivariable) calculus and a rudimentary knowledge of differentiable manifolds, including some facility in working with the basic tools of manifold theory: tensors, differential forms, Lie and covariant derivatives, multiple integrals, and so on. Although in overall content this book necessarily overlaps the several available excellent books on manifold theory, there are differences in presentation and emphasis which, it is hoped, will make it particularly suitable as an introductory text.