Summary: DIFFERENTIAL GEOMETRY:
A First Course in
Curves and Surfaces
Preliminary Version
Fall, 2011
Theodore Shifrin
University of Georgia
Dedicated to the memory of Shiing-Shen Chern,
my adviser and friend
c 2011 Theodore Shifrin
No portion of this work may be reproduced in any form without written permission of the author.
CONTENTS
1. CURVES . . . . . . . . . . . . . . . . . . . . 1
1. Examples, Arclength Parametrization 1
2. Local Theory: Frenet Frame 10
3. Some Global Results 23
2. SURFACES: LOCAL THEORY . . . . . . . . . . . . 35
1. Parametrized Surfaces and the First Fundamental Form 35
2. The Gauss Map and the Second Fundamental Form 44
3. The Codazzi and Gauss Equations and the Fundamental Theorem of

Source: Alexeev, Valery - Department of Mathematics, University of Georgia

Collections: Mathematics