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" Geometry and Algebra of Multidimensional Three-Webs "
by Maks A. Akivis, Alexander M. Shelekhov.
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BL
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| Record Number
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579570
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b408789
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| Main Entry
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Akivis, Maks A.
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| Title & Author
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Geometry and Algebra of Multidimensional Three-Webs\ by Maks A. Akivis, Alexander M. Shelekhov.
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| Publication Statement
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Dordrecht :: Springer Netherlands :: Imprint: Springer,, 1992.
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| Series Statement
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Mathematics and Its Applications (Soviet Series),; 82
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| ISBN
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9789401124027
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: 9789401050593
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| Contents
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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.
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| Abstract
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·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.
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Mathematics.
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Geometry, Algebraic.
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Algebra.
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Global differential geometry.
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| Added Entry
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Shelekhov, Alexander M.
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SpringerLink (Online service)
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