ENGLISH

Projective Differential Geometry of Submanifolds

By M.A. Akivis , V.V. Goldberg,

Book information

Publisher
Elsevier, Academic Press
Year
1993
ISBN
0444897712, 9780444897718, 9780080887166
ISSN
0924-6509
LCC
QA649 .A38 1993
Open Library ID
OL1402741M
Language
english
Format
PDF
Filesize
13 MB (14105628 bytes)
Series
North-Holland Mathematical Library 49
Edition
1
Pages
374\375
Time added
2011-06-04 13:46:07

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.

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