عنوان

Geometry and Algebra of Multidimensional Three-Webs

(Number (ISBN

9789401050593

(Number (ISBN

9789401124027

Number

b408789

Title Proper

Geometry and Algebra of Multidimensional Three-Webs

General Material Designation

[Book]

First Statement of Responsibility

by Maks A. Akivis, Alexander M. Shelekhov.

Place of Publication, Distribution, etc.

Dordrecht :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

1992.

Series Title

Mathematics and Its Applications (Soviet Series),

Volume Designation

82

ISSN of Series

0169-6378 ;

Text of Note

1 Three-Webs and Geometric Structures Associated with Them -- 1.1 G-Structures, Fibrations and Foliations -- 1.2 Three-Webs on Smooth Manifolds -- 1.3 Geometry of the Tangent Space of a Multidimensional Three-Web -- 1.4 Structure Equations of a Multidimensional Three-Web -- 1.5 Parallelizable and Group Three-Webs -- 1.6 Computation of the Torsion and Curvature Tensors of a Three-Web -- 1.7 The Canonical Chern Connection on a Three-Web -- 1.8 Other Connections Associated with a Three-Web -- 1.9 Subwebs of Multidimensional Three-Webs -- Problems -- Notes -- 2 Algebraic Structures Associated with Three-Webs -- 2.1 Quasigroups and Loops -- 2.2 Configurations in Abstract Three-Webs -- 2.3 Identities in Coordinate Loops and Closure Conditions -- 2.4 Local Differentiable Loops and Their Tangent Algebras -- 2.5 Tangent Algebras of a Multidimensional Three-Web -- 2.6 Canonical Coordinates in a Local Analytic Loop -- 2.7 Algebraic Properties of the Chern Connection -- Problems -- Notes -- 3 Transversally Geodesic and Isoclinic Three-Webs -- 3.1 Transversally Geodesic and Hexagonal Three-Webs -- 3.2 Isoclinic Three-Webs -- 3.3 Grassmann Three-Webs -- 3.4 An Almost Grassmann Structure Associated with a Three-Web. Problems of Grassmannization and Algebraization -- 3.5 Isoclinicly Geodesic Three-Webs. Three-Webs over Algebra -- Problems -- Notes -- 4 The Bol Three-Webs and the Moufang Three-Webs -- 4.1 The Bol Three-Webs -- 4.2 The Isoclinic Bol Three-Webs -- 4.3 The Six-Dimensional Bol Three-Webs -- 4.4 The Moufang Three-Webs -- 4.5 The Moufang Three-Web of Minimal Dimension -- Problems -- Notes -- 5 Closed G-Structures Associated with Three-Webs -- 5.1 Closed G-Structures on a Smooth Manifold -- 5.2 Closed G-Structures Defined by Multidimensional Three-Webs -- 5.3 Four-dimensional Hexagonal Three-Webs -- 5.4 The Closure of The G-Structure Defined by a Multidimensional Hexagonal Three-Web -- 5.5 Three-Webs and Identities in Loops -- Problems -- Notes -- 6 Automorphisms of Three-Webs -- 6.1 The Autotopies of Quasigroups and Three-Webs -- 6.2 Infinitesimal Automorphisms of Three-Webs -- 6.3 Regular Infinitesimal Automorphisms of Three-Webs -- 6.4 G-Webs -- Problems -- Notes -- 7 Geometry of the Fourth Order Differential Neighborhood of a Multidimensional Three-Web -- 7.1 Computation of Covariant Derivatives of the Curvature Tensor of a Three-Web -- 7.2 Internal Mappings in Coordinate Loops of a Three-Web -- 7.3 An Algebraic Characterization of the Tangent W4-Algebra of a Three-Web -- 7.4 Classification of Three-Webs in the Fourth Order Differential Neighborhood -- 7.5 Three-Webs with Elastic Coordinate Loop -- Problems -- Notes -- 8 d-Webs of Codimension r -- 8.1 (n + 1)-Webs on a Manifold of Dimension nr -- 8.2 (n + 1)-Webs on a Grassmann Manifold -- 8.3 (n + 1)-Webs and Almost Grassmann Structures -- 8.4 Transversally Geodesic and Isoclinic (n + 1)-Webs -- 8.5 d-Webs on a Manifold of Dimension nr -- 8.6 The Algebraization Problem for Multidimensional d-Webs -- 8.7 The Rank Problem for d-Webs -- Problems -- Notes -- Appendix A -- Symbols Frequently Used.

0

Text of Note

·Et moi, ... , Ii j'avait so comment en revenir. je One serviee mathematics has rendered the n 'y serais point all~.' human nee. It hal put rommon sense back Jules Verne whme it belongs, on the topmost shelf next to the dusty canister labelled' discarded nonsense'. The series il divergent; therefore we may be EricT. Bell able to do scmething with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics ... '; 'One service logic has rendered computer science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

International Standard Book Number

9789401050593

Title

Springer eBooks

Algebra.

Geometry, Algebraic.

Global differential geometry.

Mathematics.

Akivis, Maks A.

Shelekhov, Alexander M.

SpringerLink (Online service)

Date of Transaction

20190301082600.0

Electronic name

[Book]

Y