Projective differential geometry of submanifolds /

In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization...

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Bibliographic Details
Main Author: Akivis, M. A. (Maks Aĭzikovich)
Corporate Author: ScienceDirect (Online service)
Other Authors: Golʹdberg, V. V. (Vladislav Viktorovich)
Format: eBook
Language:English
Published: Amsterdam ; New York : North-Holland, 1993.
Series:North-Holland mathematical library ; 49.
Subjects:
Online Access:Connect to the full text of this electronic book
Description
Summary:In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
Physical Description:1 online resource (xi, 362 pages) : illustrations
Bibliography:Includes bibliographical references (pages 297-331) and index.
ISBN:9780444897718
0444897712
9780080887166
0080887163
1281778982
9781281778987