This book, based on a graduate course on Riemannian geometry and analysis on manifolds, given in Paris, covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features on the subject. Classical results on the relations between curvature and topology are treated in detail. The book is quite self-contained, assuming of the reader only a knowledge of differential calculus in Euclidean space. It contains numerous exercises with full solutions and a series of detailed examples which are picked up again repeatedly to illustrate each new definition or property introduced. This book addresses both the graduate student wanting to learn Riemannian geometry, and also the professional mathematician from a neighbouring field who needs information about ideas and techniques which are now pervading many parts of mathematics.

本文的引用網址: