Differential Geometry of Varieties with Degenerate Gauss Maps

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 st...

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Bibliographic Details
Main Authors: Akivis, Maks A., Goldberg, Vladislav V. (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 2004, 2004
Edition:1st ed. 2004
Series:CMS Books in Mathematics, Ouvrages de mathématiques de la SMC
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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505 0 |a 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 
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520 |a 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