Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition

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Courier Dover Publications, Dec 14, 2016 - Mathematics - 512 pages
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One of the most widely used texts in its field, this volume introduces the differential geometry of curves and surfaces in both local and global aspects. The presentation departs from the traditional approach with its more extensive use of elementary linear algebra and its emphasis on basic geometrical facts rather than machinery or random details. Many examples and exercises enhance the clear, well-written exposition, along with hints and answers to some of the problems.

The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the Gauss map, the intrinsic geometry of surfaces, and global differential geometry. Suitable for advanced undergraduates and graduate students of mathematics, this text's prerequisites include an undergraduate course in linear algebra and some familiarity with the calculus of several variables. For this second edition, the author has corrected, revised, and updated the entire volume.†

 

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Review: Differential Geometry of Curves and Surfaces

User Review  - Mark Hoyle - Goodreads

Excellent treatise on curves and surfaces with very clear exposition of the motivation behind many concepts in Riemannian Geometry. Read full review

Contents

Curves
1
RegularSurfaces
53
A Brief Review of Continuity and Differentiability
120
The Intrinsic Geometry of Surfaces
220
Curves and Surfaces
315
GlobalDifferentialGeometry
321
PointSet Topology of Euclidean Spaces
460
Bibliography and Comments
475
Index
503
Copyright

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About the author (2016)

Manfredo P. do Carmo is a Brazilian mathematician and authority in the very active field of differential geometry. He is an emeritus researcher at Rio's National Institute for Pure and Applied Mathematics and the author of Differential Forms and Applications.

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