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" Differential geometry of varieties with degenerate Gauss maps / "
Maks A. Akivis, Vladislav V. Goldberg
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BL
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| Record Number
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655358
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dltt
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| Main Entry
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Akivis, M. A., (Maks Aĭzikovich)
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| Title & Author
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Differential geometry of varieties with degenerate Gauss maps /\ Maks A. Akivis, Vladislav V. Goldberg
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| Series Statement
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CMS books in mathematics ;; v. 18
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| Page. NO
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xxi, 255 pages :: illustrations ;; 24 cm
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| ISBN
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0387404635
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: 9780387404639
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| Bibliographies/Indexes
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Includes bibliographical references (pages 221-236) and indexes
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| Contents
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1. Foundational material -- 1.1 Vector space -- 1.2 Differentiable manifolds -- 1.3 Projective space -- 1.4 Specializations of moving frames -- 1.5 Some algebraic manifolds -- 2. Varieties in projective spaces and their Gauss maps -- 2.1 Varieties in a projective space -- 2.2 The second fundamental tensor and the second fundamental form -- 2.3 Rand and defect of varieties with degenerate Gauss maps -- 2.4 Examples of varieties with degenerate Gauss maps -- 2.5 Application of the duality principle -- 2.6 Hypersurface with a degenerate Gauss map associated with a Veronese variety -- 3. Basic equations of varieties with degenerate Gauss maps -- 3.1 The Monge-Ampère foliation -- 3.2 Focal images -- 3.3 Some algebraic hypersurfaces with degenerate Gauss maps in P⁴ -- 3.4 The Sacksteder-Bourgain hypersurface -- 3.5 Complete varieties with degenerate Gauss maps in real projective and non-Euclidean spaces -- 4. Main structure theorems -- 4.1 Torsal varieties -- 4.2 Hypersurfaces with degenerate Gauss maps -- 4.3 Cones and affine analogue of the Hartman-Nirenberg cylinder theorem -- 4.4 Varieties with degenerate Gauss maps with multiple foci and twisted cones -- 4.5 Reducible varieties with degenerate Gauss maps -- 4.6 Embedding theorems for varieties with degenerate Gauss maps -- 5. Further examples and applications of the theory of varieties with degenerate Gauss maps -- 5.1 Lightlike hypersurfaces in the de Sitter space and their focal properties -- 5.2 Induced connections on submanifolds -- 5.3 Varieties with degenerate Gauss maps associated with smooth lines on projective planes over two-dimensional algebras
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| Abstract
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"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."--BOOK JACKET
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| Subject
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Geometry, Differential
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| Subject
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Gauss maps
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Geometri, Diferensiyel
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Gauss haritaları
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| Dewey Classification
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516.3/6
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| LC Classification
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QA641.A588 2004
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| Added Entry
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Golʹdberg, V. V., (Vladislav Viktorovich)
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