Projective Differential Geometry of Submanifolds

Projective Differential Geometry of Submanifolds

Author: M.A. Akivis

Publisher: Elsevier

ISBN: 0080887163

Category: Mathematics

Page: 361

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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.
Projective Differential Geometry of Submanifolds
Language: en
Pages: 361
Authors: M.A. Akivis, V.V. Goldberg
Categories: Mathematics
Type: BOOK - Published: 1993-06-30 - Publisher: Elsevier

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
Symposium on the Differential Geometry of Submanifolds
Language: en
Pages: 264
Authors: Luc Vrancken
Categories: Mathematics
Type: BOOK - Published: 2008-06-30 - Publisher: Lulu.com

This book contains the proceedings of the «Symposium on differential geometry» which took place at the Université de Valenciennes et du Hainaut Cambrésis from July 3, 2007 until July 7, 2007.The main theme of the conference was the differential geometry of submanifolds. Special emphasis was put on the following topics:Lagrangian
Differential Geometry Of Warped Product Manifolds And Submanifolds
Language: en
Pages: 516
Authors: Chen Bang-yen
Categories: Mathematics
Type: BOOK - Published: 2017-05-29 - Publisher: World Scientific

A warped product manifold is a Riemannian or pseudo-Riemannian manifold whose metric tensor can be decomposed into a Cartesian product of the y geometry and the x geometry — except that the x-part is warped, that is, it is rescaled by a scalar function of the other coordinates y. The
Geometry of Submanifolds
Language: en
Pages: 192
Authors: Bang-Yen Chen
Categories: Mathematics
Type: BOOK - Published: 2019-06-12 - Publisher: Courier Dover Publications

The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and
Differential Geometry of Submanifolds
Language: en
Pages: 136
Authors: K. Kenmotsu
Categories: Mathematics
Type: BOOK - Published: 2007-01-05 - Publisher: Springer

Books about Differential Geometry of Submanifolds