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| PROJECTIVE DIFFERENTIAL GEOMETRY OF SUBMANIFOLDS, 49
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By
M.A. Akivis, Moscow Institute of Steel and Alloys, Department of Mathematics, Moscow, Russia
V.V. Goldberg, New Jersey Institute of Technology, Department of Mathematics, Newark, NJ, USA
Included in series
North-Holland Mathematical Library, 49
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.
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.
| Bibliographic details |
Hardbound, 0 pages, publication date: JUN-1993
ISBN-13: 978-0-444-89771-8
ISBN-10: 0-444-89771-2
Imprint: NORTH-HOLLAND
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| Price and Ordering |
Price:
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Last update: 4 Sep 2009
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