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Differential Geometry of Varieties with Degenerate Gauss Maps

Differential Geometry of Varieties with Degenerate Gauss Maps Cover

 

Synopses & Reviews

Publisher Comments:

 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.

Synopsis:

This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate 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.

Table of Contents

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.

Product Details

ISBN:
9780387404639
Publisher:
Springer
Location:
New York
Author:
Goldberg, Vladislav
Author:
Goldberg, Vladislav V.
Author:
Akivis, Maks
Author:
Akivis, M. A.
Author:
Akivis, Maks A.
Subject:
Geometry - Differential
Subject:
Gauss maps.
Subject:
Differential geometry
Subject:
Mathematics-Differential Geometry
Copyright:
Edition Description:
Book
Series:
CMS Books in Mathematics
Series Volume:
03-127
Publication Date:
20031111
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
276
Dimensions:
235 x 155 mm 540 gr

Related Subjects

Science and Mathematics » Mathematics » Differential Geometry

Differential Geometry of Varieties with Degenerate Gauss Maps
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Product details 276 pages Springer-Verlag - English 9780387404639 Reviews:
"Synopsis" by , This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate 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.
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