| 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:
|
http://hdl.handle.net/10338.dmlcz/126095 |
| . |
| 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 |
| . |
