A Panoramic View of Riemannian Geometry

  • Marcel Berger

Table of contents

About this book

Introduction

Riemannian geometry has today become a vast and important subject. This new book of Marcel Berger sets out to introduce readers to most of the living topics of the field and convey them quickly to the main results known to date. These results are stated without detailed proofs but the main ideas involved are described and motivated. This enables the reader to obtain a sweeping panoramic view of almost the entirety of the field. However, since a Riemannian manifold is, even initially, a subtle object, appealing to highly non-natural concepts, the first three chapters devote themselves to introducing the various concepts and tools of Riemannian geometry in the most natural and motivating way, following in particular Gauss and Riemann.

Keywords

Laplace-Beltrami operator Ricci flow Riemannian geometry Riemannian manifold analysis on manifolds curvature differential geometry ergodic theory geodesic flow manifold

Authors and affiliations

  • Marcel Berger
    • 1
  1. 1.Institut des Hautes Études Scientifiques IHESBures-sur-YvetteFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18245-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-65317-2
  • Online ISBN 978-3-642-18245-7
  • About this book