Skip to content

Online ordering is currently undergoing maintenance. To place orders, please call our customer service team at +61 (03) 8671 1400. We apologize for any inconvenience.

Register Sign in Wishlist
Introduction to Möbius Differential Geometry

Introduction to Möbius Differential Geometry

Part of London Mathematical Society Lecture Note Series

  • Date Published: September 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521535694

Paperback

Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

Please email academicmarketing@cambridge.edu.au to enquire about an inspection copy of this book

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers.

    • Different approaches ('models') are given for each geometric problem presented so the reader can compare: a) classical approach, b) quaternionic approach, c) Clifford algebra approach
    • Material from the classical literature is compiled into the text and many historical references are given; the reader is led to topics/questions of current research interest
    • Certain relations between geometry and integrable systems theory are discussed as well as topics in discrete differential geometry
    Read more

    Reviews & endorsements

    'One of the most attractive features of the book is the detailed discussion of discrete analogues of isothermic surfaces and orthogonal systems which were intensively studied in the last decade … The reviewed monograph will be of great interest for researchers specializing in differential geometry, geometric theory of integrable systems and other related fields.' Zentralblatt MATH

    'The book is a well-written survey of classical results from a new point of view and a nice textbook for a study of the subject.' EMS Newsletter

    'This book is a work of scholarship, communicating the author's enthusiasm for Möbius geometry very clearly. The book will serve as an introduction to Möbius geometry to newcomers, and as a very useful reference for research workers in the field.' Tom Willmore, University of Durham

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: September 2003
    • format: Paperback
    • isbn: 9780521535694
    • length: 428 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.63kg
    • contains: 36 b/w illus.
    • availability: Available
  • Table of Contents

    Introduction
    0. Preliminaries: the Riemannian point of view
    1. The projective model
    2. Application: conformally flat hypersurfaces
    3. Application: isothermic and Willmore surfaces
    4. A quaternionic model
    5. Application: smooth and discrete isothermic surfaces
    6. A Clifford algebra model
    7. A Clifford algebra model
    Vahlen matrices
    8. Applications: orthogonal systems, isothermic surfaces
    Conclusion.

  • Author

    Udo Hertrich-Jeromin, Technische Universität Berlin

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×