Riemannian Geometry

  • Sylvestre Gallot
  • Dominique Hulin
  • Jacques Lafontaine

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 1-50
  3. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 51-105
  4. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 106-179
  5. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 180-215
  6. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 216-231
  7. Back Matter
    Pages 232-286

About this book

Introduction

In this second edition, the main additions are a section devoted to surfaces with constant negative curvature, and an introduction to conformal geometry. Also, we present a -soft-proof of the Paul Levy-Gromov isoperimetric inequal­ ity, kindly communicated by G. Besson. Several people helped us to find bugs in the. first edition. They are not responsible for the persisting ones! Among them, we particularly thank Pierre Arnoux and Stefano Marchiafava. We are also indebted to Marc Troyanov for valuable comments and sugges­ tions. INTRODUCTION This book is an outgrowth of graduate lectures given by two of us in Paris. We assume that the reader has already heard a little about differential manifolds. At some very precise points, we also use the basic vocabulary of representation theory, or some elementary notions about homotopy. Now and then, some remarks and comments use more elaborate theories. Such passages are inserted between *. In most textbooks about Riemannian geometry, the starting point is the local theory of embedded surfaces. Here we begin directly with the so-called "abstract" manifolds. To illustrate our point of view, a series of examples is developed each time a new definition or theorem occurs. Thus, the reader will meet a detailed recurrent study of spheres, tori, real and complex projective spaces, and compact Lie groups equipped with bi-invariant metrics. Notice that all these examples, although very common, are not so easy to realize (except the first) as Riemannian submanifolds of Euclidean spaces.

Keywords

Minimal surface Riemannian geometry Riemannian goemetry covariant derivative curvature manifold relativity

Authors and affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 1
  • Jacques Lafontaine
    • 2
  1. 1.Ecole Polytechnique, Unité de Recherche Associée du CNRS D 0169Centre de MathématiquesPalaiseau CedexFrance
  2. 2.Départment de Mathématiques, GETODIM - Unité de Recherche Associée du CNRS 1407Université de MontpellierMontpellier Cedex 5France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-97242-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-52401-4
  • Online ISBN 978-3-642-97242-3
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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