Differential Geometry of Varieties with Degenerate Gauss Maps

  • Maks A. Akivis
  • Vladislav V. Goldberg

Part of the CMS Books in Mathematics book series (CMSBM)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Maks A. Akivis, Vladislav V. Goldberg
    Pages 1-47
  3. Maks A. Akivis, Vladislav V. Goldberg
    Pages 49-90
  4. Maks A. Akivis, Vladislav V. Goldberg
    Pages 91-134
  5. Maks A. Akivis, Vladislav V. Goldberg
    Pages 135-173
  6. Back Matter
    Pages 221-255

About this book

Introduction

 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.

Keywords

Tensor differential geometry manifold

Authors and affiliations

  • Maks A. Akivis
    • 1
  • Vladislav V. Goldberg
    • 2
  1. 1.Department of MathematicsJerusalem Institute of Technology—Machon LevJerusalemIsrael
  2. 2.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97221
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2339-4
  • Online ISBN 978-0-387-21511-2
  • Series Print ISSN 1613-5237
  • Series Online ISSN 2197-4152
  • About this book