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Connections for non-holonomic 3-webs

Vanžurová, Alena — 1997

Proceedings of the 16th Winter School "Geometry and Physics"

A non-holonomic 3-web is defined by two operators $P$ and $B$ such that $P$ is a projector, $B$ is involutory, and they are connected via the relation $P B + B P = B$ . The so-called parallelizing connection with respect to which the 3-web distributions are parallel is defined. Some simple properties of such connections are found.

Special connections on smooth 3-web manifolds

Vanžurová, Alena — 1996

Proceedings of the 15th Winter School "Geometry and Physics"

For a three-web $W$ of codimension $n$ on a differentiable manifold $M^{2 n}$ of dimension $2 n$ , the author studies the Chern connection and a family of parallelizing connections. The latter ones have a common property with the former: the web-distributions are parallel with respect to them.

Parallelisability conditions for differentiable three-webs.

Vanžurová, Alena — 1995

Archivum Mathematicum

Soldered double linear morphisms

Alena Vanžurová — 1992

Mathematica Bohemica

Our aim is to show a method of finding all natural transformations of a functor $T T^{*}$ into itself. We use here the terminology introduced in [4,5]. The notion of a soldered double linear morphism of soldered double vector spaces (fibrations) is defined. Differentiable maps $f : C_{0} \to C_{0}$ commuting with $T T^{*}$ -soldered automorphisms of a double vector space $C_{0} = V^{*} \times V \times V^{*}$ are investigated. On the set $Z_{s} (C_{0})$ of such mappings, appropriate partial operations are introduced. The natural transformations $T T^{*} \to T T^{*}$ are bijectively related with the elements...

On reducibility of double linear connections on a double vector fibration with soldering

Alena Vanžurová — 1992

Czechoslovak Mathematical Journal

Some algebraic models for differential geometry of second order [Abstract of thesis]

Alena Vanžurová — 1988

Commentationes Mathematicae Universitatis Carolinae

Differential forms on manifolds with a polynomial structure

Alena Vanžurová — 1998

Mathematica Slovaca

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...

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.

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.