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Curves and Surfaces: Second Edition
 
Sebastián Montiel Universidad de Granada, Granada, Spain
Antonio Ros Universidad de Granada, Granada, Spain
Curves and Surfaces
Hardcover ISBN:  978-0-8218-4763-3
Product Code:  GSM/69.R
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-1151-0
Product Code:  GSM/69.R.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-4763-3
eBook: ISBN:  978-1-4704-1151-0
Product Code:  GSM/69.R.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
Curves and Surfaces
Click above image for expanded view
Curves and Surfaces: Second Edition
Sebastián Montiel Universidad de Granada, Granada, Spain
Antonio Ros Universidad de Granada, Granada, Spain
Hardcover ISBN:  978-0-8218-4763-3
Product Code:  GSM/69.R
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-1-4704-1151-0
Product Code:  GSM/69.R.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-4763-3
eBook ISBN:  978-1-4704-1151-0
Product Code:  GSM/69.R.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 692009; 376 pp
    MSC: 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 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.

    This book is published in cooperation with Real Sociedád Matematica Española.
    Readership

    Undergraduate 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 Gauss-Bonnet 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 self-study.

      MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 692009; 376 pp
MSC: 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 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.

This book is published in cooperation with Real Sociedád Matematica Española.
Readership

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 Gauss-Bonnet 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 self-study.

    MAA Reviews
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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