Riemannian Geometry

  • Sylvestre Gallot
  • Dominique Hulin
  • Jacques Lafontaine

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 1-49
  3. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 51-127
  4. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 129-206
  5. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 207-243
  6. Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine
    Pages 245-262
  7. Back Matter
    Pages 263-322

About this book

Introduction

Many years have passed since the ?rst 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 - velopments. Here is not the place to relate them. The reader can consult for instance the recent book [Br5]. of our “mentor” Marcel Berger. However,R- mannian Geometry is not only a fascinating ?eld in itself. It has proved to be a precious tool in other parts of mathematics. In this respect, we can quote the major breakthroughs in four-dimensional topology which occurred in the eighties and the nineties of the last century (see for instance [L2]). These have been followed, quite recently, by a possibly successful approach to the Poincar´ e conjecture. In another direction, Geometric Group Theory, a very active ?eld nowadays (cf. [Gr6]), borrows many ideas from Riemannian or metric geometry. Butletusstophoggingthelimelight.Thisisjustatextbook.Wehopethatour point of view of working intrinsically with manifolds as early as possible, and testingeverynewnotiononaseriesofrecurrentexamples(seetheintroduction to the ?rst edition for a detailed description), can be useful both to beginners and to mathematicians from other ?elds, wanting to acquire some feeling for the subject.

Keywords

Minimal surface Riemannian geometry Riemannian goemetry covariant derivative curvature manifold relativity

Authors and affiliations

  • Sylvestre Gallot
    • 1
  • Dominique Hulin
    • 2
  • Jacques Lafontaine
    • 3
  1. 1.Institut Fourier, C.N.R.S., UMR 5582Université Grenoble 1Saint-Martin d’HèresFrance
  2. 2.Département de MathématiquesUniversité Paris XIOrsay CXFrance
  3. 3.Département de Mathématiques, C.N.R.S., UMR 5149Université Montpellier IIMontpellier CX 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18855-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20493-0
  • Online ISBN 978-3-642-18855-8
  • Series Print ISSN 0172-5939
  • About this book
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