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Curves and Surfaces
Sebastián Montiel, Antonio Ros
Price
1270.00
ISBN
9780821868805
Language
English
Pages
392
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2011
Territorial Rights
Restricted
Imprint
American Mathematical Society

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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.

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