Previous |  Up |  Next


Title: On torsion of a $3$-web (English)
Author: Vanžurová, Alena
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 120
Issue: 4
Year: 1995
Pages: 387-392
Summary lang: English
Category: math
Summary: 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 $T$. (English)
Keyword: three-web
Keyword: torsion tensor of a web
Keyword: distribution
Keyword: projector
Keyword: manifold
Keyword: connection
Keyword: web
MSC: 53A60
MSC: 53C05
idZBL: Zbl 0851.53006
idMR: MR1415086
DOI: 10.21136/MB.1995.126095
Date available: 2009-09-24T21:13:15Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] P. Nagy: On the canonical connection of a three-web.Publ. Math. Debrecen 32 (1985), 93-99. MR 0810595
Reference: [2] P. Nagy: Invariant tensor fields and the canonical connection of a 3-web.Aeq. Math. 35 (1988), 31-44. University of Waterloo, Birkhäuser Verlag, Basel. MR 0939620
Reference: [3] P. Nagy: On complete group 3-webs and 3-nets.Arch. Math. 53 (1989), 411-413. Birkhäuser Veгlag, Basel. Zbl 0696.53008, MR 1016007, 10.1007/BF01195223
Reference: [4] J. Vanžura: Integrability conditions for polynomial structures.Kódai Math. Sem. Rep. 27 (1976), 42-60. MR 0400106, 10.2996/kmj/1138847161
Reference: [5] A. Vanžurová: On (3,2, n)-webs.Acta Sci. Math. 59 (1994), 3-4. Szeged. Zbl 0828.53017, MR 1317181
Reference: [6] A. G. Walker: Almost-product stгuctures.Differential geometry, Proc. of Symp. in Pure Math.. vol. III, 1961, pp. 94-100. MR 0123993
Reference: [7] : Webs & quasigroups.(1993). Tver State University, Russia. Zbl 0776.00019


Files Size Format View
MathBohem_120-1995-4_5.pdf 318.1Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo