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Spherical Tube Hypersurfaces: Lecture Notes in Mathematics, cartea 2020

Autor Alexander Isaev
en Limba Engleză Paperback – 31 mar 2011
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).
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Specificații

ISBN-13: 9783642197826
ISBN-10: 3642197825
Pagini: 230
Ilustrații: XII, 230 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.32 kg
Ediția:2011
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Recenzii

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)

Textul de pe ultima copertă

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).

Caracteristici

This is a research monograph which is quite unique in a number of ways However, it is hard to state the main features of the book briefly for non-experts As a result, I am afraid I cannot come up with simple selling points that would be understood by the general reader and even by mathematicians who are not experts in the area of several complex variables Includes supplementary material: sn.pub/extras