Differential Geometry

Differential Geometry : Curves - Surfaces - Manifolds

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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.
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Product details

  • Paperback | 412 pages
  • 140 x 216 x 25.4mm | 471.74g
  • Providence, United States
  • English
  • Revised
  • 3rd Revised edition
  • 1470423200
  • 9781470423209
  • 716,015

Table of contents

Notations and prerequisites from analysis
Curves in $\mathbb{R}^n$
The local theory of surfaces
The intrinsic geometry of surfaces
Riemannian manifolds
The curvature tensor
Spaces of constant curvature
Einstein spaces
Solutions to selected exercises
List of notation
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About Wolfgang Kühnel

Wolfgang Kuhnel, University of Stuttgart, Germany.
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