Projective Differential Geometry of Submanifolds

Front Cover
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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About the author (1993)

Maks A. Akivis is Professor of Mathematics at the Ben-Gurion University of the Negev in Beer-Sheva, Israel, and at the Moscow Institute of Steel and Alloys in Russia.
Vladislav V. Goldberg is Distinguished Professor of Mathematics at the New Jersey Institute of Technology in Newark.
Dr. Akivis and Dr. Goldberg are the authors of numerous papers, many of which they wrote jointly. They are the authors of the book Tensor Calculus and the monograph Projective Differential Geometry of Submanifolds. In addition, Dr. Akivis is a coauthor of the monograph Geometry and Algebra of Multidimensional Three-Webs and the book Elie Cartan (1869-1951), and Dr. Goldberg is the author of the monograph Theory of Multicodimensional (n+1)-Webs.

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