Curves and Surfaces / Edition 2

Curves and Surfaces / Edition 2

by Sebastian Montiel, Antonio Ros, Donald G. Babbitt
     
 

ISBN-10: 0821847635

ISBN-13: 9780821847633

Pub. Date: 06/30/2009

Publisher: American Mathematical Society

This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces. Following the modern point of view on differential geometry, the book emphasizes the global aspects of the subject. The excellent collection of examples and exercises (with hints) will help students in learning the material. Advanced

Overview

This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces. Following the modern point of view on differential geometry, the book emphasizes the global aspects of the subject. The excellent collection of examples and exercises (with hints) will help students in learning the material. Advanced undergraduates and graduate students will find this a nice entry point to differential geometry. In order to study the global properties of curves and surfaces, it is necessary to have more sophisticated tools than are usually found in textbooks on the topic. In particular, students must have a firm grasp on certain topological theories. Indeed, this monograph treats the Gauss-Bonnet theorem and discusses the Euler characteristic. The authors also cover Alexandrov's theorem on embedded compact surfaces in $\mathbb{R}^3$ with constant mean curvature. The last chapter addresses the global geometry of curves, including periodic space curves and the four-vertices theorem for plane curves that are not necessarily convex. Besides being an introduction to the lively subject of curves and surfaces, this book can also be used as an entry to a wider study of differential geometry. It is suitable as the text for a first-year graduate course or an advanced undergraduate course. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).

Product Details

ISBN-13:
9780821847633
Publisher:
American Mathematical Society
Publication date:
06/30/2009
Series:
Graduate Studies in Mathematics Series, #69
Edition description:
New Edition
Pages:
386
Product dimensions:
7.20(w) x 10.30(h) x 1.00(d)

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