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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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发表于 2025-3-21 19:58:48 | 显示全部楼层 |阅读模式
书目名称Differential Geometry of Varieties with Degenerate Gauss Maps
编辑Maks A. Akivis,Vladislav V. Goldberg
视频video
概述Includes supplementary material:
丛书名称CMS Books in Mathematics
图书封面Titlebook: Differential Geometry of Varieties with Degenerate Gauss Maps;  Maks A. Akivis,Vladislav V. Goldberg Textbook 2004 Springer-Verlag New York
描述.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...Each author has published over 100 papers and they have each written a number of
出版日期Textbook 2004
关键词Tensor; differential geometry; manifold
版次1
doihttps://doi.org/10.1007/b97221
isbn_softcover978-1-4419-2339-4
isbn_ebook978-0-387-21511-2Series ISSN 1613-5237 Series E-ISSN 2197-4152
issn_series 1613-5237
copyrightSpringer-Verlag New York 2004
The information of publication is updating

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发表于 2025-3-21 21:10:44 | 显示全部楼层
发表于 2025-3-22 02:23:18 | 显示全部楼层
Maks A. Akivis,Vladislav V. GoldbergIncludes supplementary material:
发表于 2025-3-22 05:13:16 | 显示全部楼层
发表于 2025-3-22 11:07:42 | 显示全部楼层
https://doi.org/10.1007/978-3-8274-2859-2we consider the main topics associated with differentiable manifolds: tangent spaces, frame bundles, mappings, exterior differential calculus, Cartan’s lemma, completely integrable systems, the Frobenius theorem, Cartan’s test for a system in involution, the structure equations of a differentiable m
发表于 2025-3-22 13:05:45 | 显示全部楼层
https://doi.org/10.1007/978-3-8274-2859-2ntal tensor and the second fundamental form, and the asymptotic lines and asymptotic cone) associated with a variety in a projective space ℙ., in Section 2.3, we define the rank of a variety and varieties with degenerate Gauss maps. In Section 2.4, we consider the main examples of varieties with deg
发表于 2025-3-22 18:56:33 | 显示全部楼层
Wie der Schall soziale Räume schafftof varieties with degenerate Gauss maps, and prove a characteristic property of such varieties (the Monge—Ampère foliation has flat leaves) of any of their plane generators. At the end of Section 3.1, for varieties with degenerate Gauss maps we prove the generalized Griffiths-Harris Theorem, which b
发表于 2025-3-23 00:20:40 | 显示全部楼层
Wie der Schall soziale Räume schafftcones. For each of these types of varieties, we consider the structure of their focal images and find sufficient conditions for a variety with a degenerate Gauss map to belong to one of these types (for torsal varieties our condition is also necessary). In Theorems 4.3, 4.4, 4.5, 4.15, and 4.16, we
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