Alena Vanzurova, Department of Algebra and Geometry, Palacky University, Tomkova 40, 770 00 Olomouc, e-mail email@example.com
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, ; 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, . 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
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