Tuesday 24 July 2012

Curves and Surfaces (Second Edition) Montiel, Sebastián & Ros, Antonio

IMAGE NOT AVAILABLE


Curves and Surfaces (Second Edition)
Montiel, Sebastián & Ros, Antonio
2011; 392 pp; Paperback; 180 × 240 mm; 978-0-8218-6880-5
For sale only in India,Pakistan,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives
Series: Indian Editions of AMS Titles
720.00
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.

Table of Contents
Preface to the Second Edition
Preface to the English Edition
  1. Plane and Space Curves
  2. Surfaces in Euclidean Space
  3. The Second Fundamental Form
  4. Separation and Orientability
  5. Integration on Surfaces
  6. Global Extrinsic Geometry
  7. Intrinsic Geometry of Surfaces
  8. The Gauss-Bonnet Theorem
  9. Global Geometry of Curves
Bibliography
Index

About the Author
Sebastián Montiel is Professor of Geometry and Topology, University of Granada Antonio Ros belongs to the Department of Geometry Granada University

No comments:

Post a Comment