[Book Cover]

Differential Geometry of Curves and Surfaces, 1/e

Manfredo DoCarmo, Instituto de Matematica Pura e Aplicada

Published February, 1976 by Prentice Hall Engineering/Science/Mathematics

Copyright 1976, 503 pp.
ISBN 0-13-212589-7

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This volume covers local as well as global differential geometry of curves and surfaces.


makes extensive use of elementary linear algebra — with emphasis on basic geometrical facts rather than on machinery or random details.
stresses the basic ideas of differential geometry — regular surfaces, the Gauss map, covariant derivatives.
includes a large number of fully-worked examples.

Table of Contents

    1. Curves: Parametrized Curves.
    2. Regular Surfaces: Regular Surfaces; Inverse Images of Regular Values.
    3. Geometry of the Gauss Map: Definition of the Gauss Map and Its Fundamental Properties.
    4. Intrinsic Geometry of Surfaces: Isometrics; Conformal Maps.
    5. Global Differential Geometry: Rigidity of the Sphere.


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