Projective differential geometry of submanifolds
Author(s)
Bibliographic Information
Projective differential geometry of submanifolds
（North-Holland mathematical library, 49）
North-Holland, 1993
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Note
Includes bibliographical references (p. 297-331) and index
Description and Table of Contents
Description
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.
Table of Contents
Preface. Chapters: 1. Preliminaries. 2. The Foundations of Projective Differential Geometry of Submanifolds. 3. Submanifolds Carrying a Net of Conjugate Lines. 4. Tangentially Degenerate Submanifolds. 5. Submanifolds with Asymptotic and Conjugate Distributions. 6. Normalized Submanifolds in a Projective Space. 7. Projective Differential Geometry of Hypersurfaces. 8. Algebraization Problems in Projective Differential Geometry.Bibliography. Symbols Frequently Used. Index.
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