Differential Geometry: Manifolds, Curves, and Surfaces

• Marcel Berger
• Bernard Gostiaux
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 115)

1. Front Matter
Pages i-xii
2. Marcel Berger, Bernard Gostiaux
Pages 1-29
3. Marcel Berger, Bernard Gostiaux
Pages 30-46
4. Marcel Berger, Bernard Gostiaux
Pages 47-102
5. Marcel Berger, Bernard Gostiaux
Pages 103-127
6. Marcel Berger, Bernard Gostiaux
Pages 128-145
7. Marcel Berger, Bernard Gostiaux
Pages 146-187
8. Marcel Berger, Bernard Gostiaux
Pages 188-243
9. Marcel Berger, Bernard Gostiaux
Pages 244-276
10. Marcel Berger, Bernard Gostiaux
Pages 277-311
11. Marcel Berger, Bernard Gostiaux
Pages 312-345
12. Marcel Berger, Bernard Gostiaux
Pages 346-402
13. Marcel Berger, Bernard Gostiaux
Pages 403-441
14. Back Matter
Pages 443-476

Introduction

This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ­ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc­ tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.

Keywords

Gaussian curvature Mean curvature Minimal surface curvature differential geometry manifold

Authors and affiliations

• Marcel Berger
• 1
• Bernard Gostiaux
• 2
1. 1.I.H.E.S.Bures-sur-YvetteFrance
2. 2.Le PerreuxFrance

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-1033-7
• Copyright Information Springer-Verlag New York Inc. 1988
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-6992-2
• Online ISBN 978-1-4612-1033-7
• Series Print ISSN 0072-5285