**Student Mathematical Library**

Volume: 77;
2015;
403 pp;
Softcover

MSC: Primary 53;

Print ISBN: 978-1-4704-2320-9

Product Code: STML/77

List Price: $49.00

Individual Price: $39.20

**Electronic ISBN: 978-1-4704-2675-0
Product Code: STML/77.E**

List Price: $49.00

Individual Price: $39.20

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# Differential Geometry: Curves — Surfaces — Manifolds, Third Edition

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*Wolfgang Kühnel*

This carefully written book is an introduction to the beautiful ideas and results of differential geometry. The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. The second part studies the geometry of general manifolds, with particular emphasis on connections and curvature. The text is illustrated with many figures and examples. The prerequisites are undergraduate analysis and linear algebra. This new edition provides many advancements, including more figures and exercises, and—as a new feature—a good number of solutions to selected exercises.

This new edition is an improved version of what was already an excellent and carefully written introduction to both differential geometry and Riemannian geometry. In addition to a variety of improvements, the author has included solutions to many of the problems, making the book even more appropriate for use in the classroom.

—Colin Adams, Williams College

This book on differential geometry by Kühnel is an excellent and useful introduction to the subject. … There are many points of view in differential geometry and many paths to its concepts. This book provides a good, often exciting and beautiful basis from which to make explorations into this deep and fundamental mathematical subject.

— Louis Kauffman, University of Illinois at Chicago

#### Table of Contents

# Table of Contents

## Differential Geometry: Curves -- Surfaces -- Manifolds, Third Edition

- Cover Cover11
- Title page iii4
- Contents v6
- Preface to the English edition ix10
- Preface to the German edition xi12
- Chapter 1. Notations and prerequisites from analysis 114
- Chapter 2. Curves in ℝⁿ 720
- Chapter 3. The local theory of surfaces 5568
- Chapter 4. The intrinsic geometry of surfaces 133146
- Chapter 5. Riemannian manifolds 197210
- Chapter 6. The curvature tensor 233246
- Chapter 7. Spaces of constant curvature 265278
- Chapter 8. Einstein spaces 309322
- Solutions to selected exercises 361374
- Bibliography 391404
- List of notation 395408
- Index 397410
- Copying and reprinting notice 403416
- Other titles in this series 404417
- Back Cover Back Cover1418

#### Readership

Undergraduate and graduate students interested in differential geometry.