
Preface  Preview Material  Table of Contents  Supplementary Material 
Graduate Studies in Mathematics 2009; 376 pp; hardcover Volume: 69 ISBN10: 0821847635 ISBN13: 9780821847633 List Price: US$73 Member Price: US$58.40 Order Code: GSM/69.R See also: Differential Geometry: Curves  Surfaces  Manifolds, Second Edition  Wolfgang Kuhnel Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems  Thomas A Ivey and J M Landsberg A Course in Differential Geometry  Thierry Aubin  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 GaussBonnet 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 fourvertices 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 firstyear graduate course or an advanced undergraduate course. Request an examination or desk copy. This book is published in cooperation with Real Sociedad Matemática Española (RSME). Readership Undergraduate students, graduate students, and research mathematicians interested in the geometry of curves and surfaces. Reviews "With its readable style and the completeness of its exposition, this would be a very good candidate for an introductory graduate course in differential geometry or for selfstudy."  MAA Reviews 


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