Spherical tube hypersurfaces
 Responsibility
 Alexander Isaev.
 Digital
 text file
 Imprint
 Berlin ; Heidelberg ; New York : Springer, ©2011.
 Physical description
 1 online resource (xii, 220 pages)
 Series
 Lecture notes in mathematics (SpringerVerlag) ; 2020.
Online
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Description
Creators/Contributors
 Author/Creator
 Isaev, Alexander.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Machine generated contents note:
 1.1. Introduction to CRManifolds
 1.2. Chern's Construction
 1.3. Chern's Invariants on Section of Bundle P2 > M
 1.4. Umbilicity
 2.1. Zero CRCurvature Equations for Rigid Hypersurfaces
 2.2. Application
 3.1. Zero CRCurvature Equations for Tube Hypersurfaces
 3.2. Analyticity of Spherical Tube Hypersurfaces
 4.1. Classification of Defining Systems
 4.2. Defining Systems of Type I
 4.3. Defining Systems of Type II
 4.4. Defining Systems of Type III
 4.5. Globalization of Spherical Tube Hypersurfaces
 5.1. Defining Systems of Type I
 5.2. Defining Systems of Type III
 5.3. Classification
 6.1. Real Canonical Forms of Pair of Matrices Q, X, where Q is Symmetric and X is QSymmetric
 6.2. Defining Systems of Type II
 6.3. Defining Systems of Type III
 6.4. Defining Systems of Type I
 6.5. Classification
 7.1. Classification
 7.2. Defining Systems of Type II
 7.3. Defining Systems of Type III
 7.4. Defining Systems of Type 1
 8.1. Statement of Results
 8.2. Proof of Theorem 8.1
 8.3. Proof of Theorem 8.2
 9.1. Tube Hypersurfaces with Degenerate Levi Form
 9.1.1. Complex Foliations on CRManifolds 195
 9.1.2. Levi Foliation on Tube Manifold
 9.2. Approach of G. Fels and W. Kaup.
 Publisher's summary

We consider Levi nondegenerate tube hypersurfaces in complex linear space which are "spherical", that is, locally CRequivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CRcurvature form, so such hypersurfaces are flat from the CRgeometric 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 twofold: CRgeometric and affinegeometric. Spherical tube hypersurfaces turn out to possess remarkable properties. For example, every such hypersurface is realanalytic and extends to a closed realanalytic 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).
(source: Nielsen Book Data)
Subjects
 Subjects
 Hypersurfaces.
Bibliographic information
 Publication date
 2011
 Series
 Lecture notes in mathematics ; 2020
 ISBN
 9783642197833 (electronic bk.)
 3642197833 (electronic bk.)
 3642197825
 9783642197826
 9783642197826
 DOI
 10.1007/9783642197833