# [share_ebook] Curves and Surfaces (Graduate Studies in Mathematics)

#### 作者: Sebastián Montiel and Antonio Ros

#### 日期: 2011-09-25

#### 页数: 376

#### 出版社: American Mathematical Society, Real Sociedad Matem\'{a}tica Espa\~{n}ola (RSME)

#### 标签: 数学

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**Curves and Surfaces (Graduate Studies in Mathematics)**

Sebastián Montiel and Antonio Ros | American Mathematical Society, Real Sociedad Matem\'{a}tica Espa\~{n}ola (RSME) | 2011-09-25 | 376 pages | English | PDF

This introductory textbook puts forth a clear and focused point of view on the differential geometry of curves and surfaces, emphasizing the global aspects. 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.

This volume is suitable for advanced undergraduates, graduate students, and researchers interested in the differential geometry of curves and surfaces. It can also be used as an introduction to a more general study of differential geometry.

This book is jointly published by the AMS and the Real Sociedad Matemática Española (RSME).

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