Differential Geometry of Varieties with Degenerate Gauss Maps

Maks A. Akivis, Vladislav V. Goldberg - Collection CMS Books in Mathematics

255 pages, parution le 31/12/2003

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Résumé

In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps. The authors introduce the above mentioned methods and apply them to a series of concrete problems arising in the theory of varieties with degenerate Gauss maps. What makes this book unique is the authors? use of a systematic application of methods of projective differential geometry along with methods of the classical algebraic geometry for studying varieties with degenerate Gauss maps. This book is intended for researchers and graduate students interested in projective differential geometry and algebraic geometry and their applications. It can be used as a text for advanced undergraduate and graduate students. Each author has published over 100 papers and they have each written a number of books, including Conformal Differential Geometry and Its Generalizations (Wiley 1996), Projective Differential Geometry of Submanifolds (North-Holland 1993), and Introductory Linear Algebra (Prentice-Hall 1972), which were written by them jointly.

Written for:
2nd year graduate students, mathematics researchers

Sommaire

Preface
Foundational Material
Varieties in Projective Spaces and Their Gauss Maps
Basic Equations of Varieties with Degenerate Gauss Maps
Main Structure Theorems
Further Examples and Applications of the Theory of Varieties with Degenerate Gauss Maps
Bibliography
Symbols Frequently Used
Author Index
Subject Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Maks A. Akivis, Vladislav V. Goldberg
Collection	CMS Books in Mathematics
Parution	31/12/2003
Nb. de pages	255
Format	16 x 24
Couverture	Relié
Poids	515g
Intérieur	Noir et Blanc
EAN13	9780387404639
ISBN13	978-0-387-40463-9