Differential Geometry of Varieties with Degenerate Gauss Maps (CMS Books in Mathematics) - Hardcover

Akivis, Maks A.; Goldberg, Vladislav V.

Hardcover

ISBN 10: 0387404635 ISBN 13: 9780387404639

Publisher: Springer, 2003

Synopsis

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.

About this title

From the Back Cover

 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.

Edition details

• Publisher: Springer
• Publication date: 2003
• Language: English
• ISBN 10: 0387404635
• ISBN 13: 9780387404639
• Binding: Hardcover
• Number of pages: 276