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On torsion of a 3 -web

Alena Vanžurová (1995)

Mathematica Bohemica

A 3-web on a smooth 2 n -dimensional manifold can be regarded locally as a triple of integrable n -distributions which are pairwise complementary, [5]; that is, we can work on the tangent bundle only. This approach enables us to describe a 3 -web and its properties by invariant ( 1 , 1 ) -tensor fields P and B where P is a projector and B 2 = id. The canonical Chern connection of a web-manifold can be introduced using this tensor fields, [1]. Our aim is to express the torsion tensor T of the Chern connection through...

Parallelisability conditions for differentiable three-webs

Alena Vanžurová (1995)

Archivum Mathematicum

Our aim is to find conditions under which a 3-web on a smooth 2 n -dimensional manifold is locally equivalent with a web formed by three systems of parallel n -planes in R 2 n . We will present here a new approach to this “classical” problem using projectors onto the distributions of tangent subspaces to the leaves of foliations forming the web.

Solution of Belousov's problem

Maks A. Akivis, Vladislav V. Goldberg (2001)

Discussiones Mathematicae - General Algebra and Applications

The authors prove that a local n-quasigroup defined by the equation x n + 1 = F ( x , . . . , x ) = ( f ( x ) + . . . + f ( x ) ) / ( x + . . . + x ) , where f i ( x i ) , i,j = 1,...,n, are arbitrary functions, is irreducible if and only if any two functions f i ( x i ) and f j ( x j ) , i ≠ j, are not both linear homogeneous, or these functions are linear homogeneous but f i ( x i ) / x i f j ( x j ) / x j . This gives a solution of Belousov’s problem to construct examples of irreducible n-quasigroups for any n ≥ 3.

Tensor approach to multidimensional webs

Alena Vanžurová (1998)

Mathematica Bohemica

An anholonomic ( n + 1 ) -web of dimension r is considered as an ( n + 1 ) -tuple of r -dimensional distributions in general position. We investigate a family of ( 1 , 1 ) -tensor fields (projectors and nilpotents associated with a web in a natural way) which will be used for characterization of all linear connections on a manifold preserving the given web.

Tissus plans exceptionnels et fonctions thêta

Luc Pirio, Jean-Marie Trépreau (2005)

Annales de l'institut Fourier

Dans cet article, nous présentons une famille à un paramètre de 5-tissus plans exceptionnels. Dans leur présentation la plus naturelle, les tissus de cette famille sont formés d’un système harmonique de quatre pinceaux de droites parallèles et du feuilletages d’intégrale première, la fonction sn k x sn k y , où sn k est une fonction elliptique de Jacobi.

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