Maks A. Akivis, Vladislav V. Goldberg

Differential Geometry of Varieties with Degenerate Gauss Maps (eBook, PDF)

• Format: PDF

Produktbeschreibung

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 method of moving frames and exterior differential forms as well as tensor methods. This book is intended for researchers and graduate students who are interested in projective differential geometry and algebraic geometry and their applications.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 255
• Erscheinungstermin: 18. April 2006
• Englisch
• ISBN-13: 9780387215112
• Artikelnr.: 43998766

Autorenporträt

Maks Akivis, Jerusalem Institute of Technology, Machon Lev, Jerusalem, Israel / Vladislav Goldberg, New Jersey Institute of Technology, Newark, NJ, USA

Inhaltsangabe

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.

Rezensionen

From the reviews:

"The study of the Gauss map of algebraic varieties falls into the fields of the so-called projective-differential geometry. ... the authors show their mastery of the Cartan method, stating and proving the most interesting results. ... this book has a very ample and generally accurate bibliography ... . This provides an excellent reference for the interested researcher. ... this book is recommended for people interested in differential geometry and in projective differential geometry, wishing to learn the methods of E. Cartan." (Emilia Mezzetti, SIAM Review, Vol. 48 (1), 2006)

"The present authors first aim at an extension of the motion of a variety to the real C⁸ -category and, secondly, embark on a theory for varieties with degenerate Gauss map, including several structure theorems and a lot of concrete situations. ... is of high interest for specialists who find in it a comprehensive study on degenerate Gauss maps in projective space if they are willing to look after necessary assumptions and foundations ... . The book has an ample bibliography of about 180 items." (Rolf Walter, Zentralblatt MATH, Vol. 1114 (16), 2007)