Curves and Surfaces: No. 69 (Graduate Studies in Mathematics) - Hardcover

Montiel, Sebastian; Ros, Antonio

Hardcover

ISBN 10: 0821838156 ISBN 13: 9780821838150

Verlag: American Mathematical Society, 2005

Inhaltsangabe

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.

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Reseña del editor

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. Information for our distributors: This book is jointly published by the AMS and the Real Sociedad Matematica Espanola (RSME).

Details zur Ausgabe

• Verlag: American Mathematical Society
• Erscheinungsdatum: 2005
• Sprache: Englisch
• ISBN 10: 0821838156
• ISBN 13: 9780821838150
• Einband: Tapa dura
• Anzahl der Seiten: 376
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar