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Spherical Tube Hypersurfaces

Name: Spherical Tube Hypersurfaces
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 04416687
Price: 45.49 EUR
Availability: InStock
Author: Isaev
ISBN: 9783642197826

Isaev

Language

English

Book Paperback

Libristo code: 04416687

Publishers Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, March 2011

We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical", th... Full description

Libristo code: 04416687

111 b

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We consider 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 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. Spherical tube hypersurfaces turn out to 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 give 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 due to G. Fels and W. Kaup (2009).