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.
General
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