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Introduction to Möbius Differential Geometry

Introduction to Möbius Differential Geometry

$88.99 (C)

Part of London Mathematical Society Lecture Note Series

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

$ 88.99 (C)

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About the Authors
  • This introduction to the conformal differential geometry of surfaces and submanifolds covers those aspects of the geometry of surfaces that only refer to an angle measurement, but not to a length measurement. Different methods (models) are presented for analysis and computation. Various applications to areas of current research are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.

    • 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    • Material from the classical literature is compiled into the text and many historical references are given; the reader is led to topics/questions of current research interest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
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    Reviews & endorsements

    "...carefully written with detailed references, extensive historical notes and helpful comments at the beginning of each new chapter. It is an outstanding introduction to a classical field which has taken on new life over the past quarter century, and it is highly recommended by the viewer." Bulletin of the AMS

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    Product details

    • Date Published: August 2003
    • format: Paperback
    • isbn: 9780521535694
    • length: 428 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.582kg
    • contains: 36 b/w illus.
    • availability: Available
  • Table of Contents

    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

  • Author

    Udo Hertrich-Jeromin, Technische Universität Berlin

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