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From the preface: Many years have passed since the first edition. However, the encouragements of various readers and friends have persuaded us to write this third edition. During these years, Riemannian Geometry has undergone many dramatic developments. Here is not the place... Read Full Overview

Traditional point of view: pinched manifolds 147 Almost flat pinching 148 Coarse point of view: compactness theorems of Gromov and Cheeger 149 K. CURVATURE AND REPRESENTATIONS OF THE ORTHOGONAL GROUP Decomposition of the space of curvature tensors 150 Conformally flat manifolds... Read Full Overview

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 of the subject. This book... Read Full Overview