Projective Differential Geometry of Submanifolds

Projective Differential Geometry of Submanifolds

1st Edition - June 30, 1993

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  • Authors: M.A. Akivis, V.V. Goldberg
  • eBook ISBN: 9780080887166

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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.

Product details

  • No. of pages: 361
  • Language: English
  • Copyright: © North Holland 1993
  • Published: June 30, 1993
  • Imprint: North Holland
  • eBook ISBN: 9780080887166

About the Authors

M.A. Akivis

Affiliations and Expertise

Moscow Institute of Steel and Alloys, Department of Mathematics, Moscow, Russia

V.V. Goldberg

Affiliations and Expertise

New Jersey Institute of Technology, Department of Mathematics, Newark, NJ, USA

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