Titlebook: Differential Geometry of Varieties with Degenerate Gauss Maps; Maks A. Akivis,Vladislav V. Goldberg Textbook 2004 Springer-Verlag New York

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Textbook 2004is 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

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1613-5237 aic 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 of978-1-4419-2339-4978-0-387-21511-2Series ISSN 1613-5237 Series E-ISSN 2197-4152

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Main Structure Theorems,d cones. We also prove here existence theorems for some varieties with degenerate Gauss maps, for example, for twisted cones in P. and A. (Theorems 4.12 and 4.14) and establish a structure of twisted cones in ℙ. (Theorems 4.13). This structure allows us to find a procedure for construction of twiste

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Further Examples and Applications of the Theory of Varieties with Degenerate Gauss Maps,ructure. In Section 5.3, we consider smooth lines on projective planes over the complete matrix algebra M of order two, the algebra ℂ of complex numbers, the algebra ℂ. of double numbers, and the algebra ℂ. of dual numbers. For the algebras ℂ, ℂ., and ℂ., in the space ℝℙ., to these smooth lines ther

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https://doi.org/10.1007/978-3-8274-2859-2rames by considering the geometry of a curve in the projective plane. Finally, in Section 1.5, we study some algebraic varieties, namely, Grassmannians and determinant submanifolds (Segre and Veronese varieties).

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Textbook 2004 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 classificati