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84,55 ۥ Cover 1Free
• Title page 5Free
• Contents 9Free
• Preface to the second edition 13Free
• Preface to the English edition 15Free
• Preface 17Free
• Plane and space curves 19Free
• Surfaces in Euclidean space49
• The second fundamental form85
• Separation and orientability125
• Integration on surfaces153
• Global extrinsic geometry189
• Intrinsic geometry of surfaces221
• The Gauss–Bonnet theorem293
• Global geometry of curves327
• Bibliography389
• Index 391Free
• Back Cover395
• Cover396
• Title page400
• Contents404
• Preface to the second edition408
• Preface to the English edition410
• Preface412
• Plane and space curves414
• Surfaces in Euclidean space444
• The second fundamental form480
• Separation and orientability520
• Integration on surfaces548
• Global extrinsic geometry584
• Intrinsic geometry of surfaces616
• The Gauss–Bonnet theorem688
• Global geometry of curves722
• Bibliography784
• Index786
• Back Cover790
• Preview Material
• Table of Contents
• Preface
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 R3R3 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.
Authors
• Sebastián Montiel: Universidad de Granada, Granada, Spain,
• Antonio Ros: Universidad de Granada, Granada, Spain
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