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Field name	Details
Dewey Class	516.36
Title	Geometry and Algebra of Multidimensional Three-Webs ([EBook] /) / by Maks A. Akivis, Alexander M. Shelekhov.
Author	Akivis, Maks A.
Added Personal Name	Shelekhov, Alexander M. author.
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands : : Imprint: Springer, , 1992.
Physical Details	XVII, 358 p. : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 82
ISBN	9789401124027
Contents 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-011-2402-7
Links to Related Works	Subject References: Algebraic Geometry . Differential Geometry . Mathematics . Non-associative Rings and Algebras . Nonassociative rings . Rings (Algebra) . Authors: Akivis, Maks A. . Shelekhov, Alexander M. . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 516.36 .

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Geometry and Algebra of Multidimensional Three-Webs

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