**
MATHEMATICA BOHEMICA, Vol. 120, No. 4, pp. 387-392, 1995
**

#
On torsion of a 3-web

##
Alena Vanzurova

* Alena Vanzurova,* Department of Algebra and Geometry, Palacky University, Tomkova 40, 770 00 Olomouc, e-mail ` vanzurov@risc.upol.cz`

**Abstract:** A 3-web on a smooth $2n$-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 the Nijenhuis $(1,2)$-tensor field $[P,B]$, and to verify that $[P,B]=0$ is a necessary and sufficient conditions for vanishing of the torsion $T$.

**Keywords:** distribution, projector, manifold, connection, web

**Classification (MSC91):** 53C05

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]