Titlebook: Geometry and Algebra of Multidimensional Three-Webs; Maks A. Akivis,Alexander M. Shelekhov Book 1992 Springer Science+Business Media Dordr

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The Bol Three-Webs and the Moufang Three-Webs,se classes can betransferred into one another if we renumber the foliations according to a parastrophytransformation of the coordinate quasigroup of a web. This allows us to study onlyone of these three classes, for example, the middle Bol webs B..

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Closed ,-Structures Associated with Three-Webs, Section 1.1.We noted there that a .-structure . in a smooth manifold . of dimension . isa subbundle of the frame bundle .(.), with the same base . as .(.), which isdefined by a Lie group . - a subgroup of the general linear group .(.). Thissubbundle can be given by differential equations (1.8). If

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和音

Geometry of the Fourth Order Differential Neighborhood of a Multidimensional Three-Web,t of all, eachof the classes of webs listed in Table 2.2 (p. 83) can be characterized by a specialstructure of the torsion and curvature tensors . and .. Secondly, these tensors have aclear geometric meaning: they determine the principal part of the “deviation” fromcommutativity and associativity in

palette

Webs of Codimension ,formed by four or morefamilies of curves in a plane as well as webs formed by families of surfaces in a three-dimensionalspace were investigated. These constructions were generalized to higherdimensions. In this way, the theory of webs formed by . foliations of codimension . ina smooth manifold . of

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防御

https://doi.org/10.1007/978-3-476-05049-6 . at the point.. Let us denote by ., ., ., . = 1,2, ... , ., local coordinates in a neighborhood .of the point . and by . and . respectively the natural basis of vector fields andthe corresponding co-basis of differential forms in .. If the vectors .forma vector frame, then the corresponding co-fra