Hardcover ISBN:  9780821847633 
Product Code:  GSM/69.R 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $62.40 
Electronic ISBN:  9781470411510 
Product Code:  GSM/69.R.E 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $58.40 

Book DetailsGraduate Studies in MathematicsVolume: 69; 2009; 376 ppMSC: Primary 53;
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 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.This book is published in cooperation with Real Sociedád Matematica Española.ReadershipUndergraduate students, graduate students, and research mathematicians interested in the geometry of curves and surfaces.

Table of Contents

Chapters

Chapter 1. Plane and space curves

Chapter 2. Surfaces in Euclidean space

Chapter 3. The second fundamental form

Chapter 4. Separation and orientability

Chapter 5. Integration on surfaces

Chapter 6. Global extrinsic geometry

Chapter 7. Intrinsic geometry of surfaces

Chapter 8. The GaussBonnet theorem

Chapter 9. Global geometry of curves


Additional Material

Reviews

This book is a nice introduction to differential geometry with contemporary emphasis on aspects of a global nature.
Mathematical 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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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 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.
Undergraduate students, graduate students, and research mathematicians interested in the geometry of curves and surfaces.

Chapters

Chapter 1. Plane and space curves

Chapter 2. Surfaces in Euclidean space

Chapter 3. The second fundamental form

Chapter 4. Separation and orientability

Chapter 5. Integration on surfaces

Chapter 6. Global extrinsic geometry

Chapter 7. Intrinsic geometry of surfaces

Chapter 8. The GaussBonnet theorem

Chapter 9. Global geometry of curves

This book is a nice introduction to differential geometry with contemporary emphasis on aspects of a global nature.
Mathematical 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