عنوان

Differential geometry of varieties with degenerate Gauss maps /

(Number (ISBN

0387404635

(Number (ISBN

9780387404639

Number

dltt

Title Proper

Differential geometry of varieties with degenerate Gauss maps /

General Material Designation

[Book]

First Statement of Responsibility

Maks A. Akivis, Vladislav V. Goldberg

Specific Material Designation and Extent of Item

xxi, 255 pages :

Other Physical Details

illustrations ;

Dimensions

24 cm

Series Title

CMS books in mathematics ;

Volume Designation

v. 18

Text of Note

Includes bibliographical references (pages 221-236) and indexes

Text of Note

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

0

Text of Note

"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

Source for Acquisition/Subscription Address

TVG

Stock Number

63346

Gauss maps

Geometry, Differential

Gauss haritaları

Geometri, Diferensiyel

QA

Number

Edition

Class number

Book number

Akivis, M. A., (Maks Aĭzikovich)

Golʹdberg, V. V., (Vladislav Viktorovich)

Date of Transaction

20160712072300.0

Electronic name

[Book]

Y