Differential Geometry

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 ...

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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.

Cover 1
Title page 4
Contents 6
Preface to the English edition 10
Preface to the German edition 12
Chapter 1. Notations and prerequisites from analysis 14
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Cover 1
Title page 4
Contents 6
Preface to the English edition 10
Preface to the German edition 12
Chapter 1. Notations and prerequisites from analysis 14
Chapter 2. Curves in ℝⁿ 20
Chapter 3. The local theory of surfaces 68
Chapter 4. The intrinsic geometry of surfaces 146
Chapter 5. Riemannian manifolds 210
Chapter 6. The curvature tensor 246
Chapter 7. Spaces of constant curvature 278
Chapter 8. Einstein spaces 322
Solutions to selected exercises 374
Bibliography 404
List of notation 408
Index 410
Copying and reprinting notice 416
Other titles in this series 417
Back Cover 418
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