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Lecture Notes in Mathematics
cover

Spherical Tube Hypersurfaces

Authors: Isaev, Alexander

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About this book

We examine Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical," that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are also of interest from the point of view of affine geometry. Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. As the book shows, spherical tube hypersurfaces possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to provide an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces, starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach put forward by G. Fels and W. Kaup (2009).

Reviews

From the book reviews:

“The main goal and purpose of Isaev’s book is to explore the invariant theory of the special class of spherical tube hypersurfaces. … this book will be of interest and of value to everyone working on the equivalence problem for CR structures.” (Thomas Garrity, Bulletin of the American Mathematical Society, Vol. 51 (4), 2014)

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Invariants of CR-Hypersurfaces

    Pages 1-33

    Isaev, Prof. Alexander

  • Rigid Hypersurfaces

    Pages 35-40

    Isaev, Prof. Alexander

  • Tube Hypersurfaces

    Pages 41-53

    Isaev, Prof. Alexander

  • General Methods for Solving Defining Systems

    Pages 55-82

    Isaev, Prof. Alexander

  • Strongly Pseudoconvex Spherical Tube Hypersurfaces

    Pages 83-96

    Isaev, Prof. Alexander

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-19783-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-642-19782-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Spherical Tube Hypersurfaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2020
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-19783-3
DOI
10.1007/978-3-642-19783-3
Softcover ISBN
978-3-642-19782-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XII, 230
Topics

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