Tensor approach to multidimensional webs
Mathematica Bohemica, Tome 123 (1998) no. 3, pp. 225-242
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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.
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.
DOI : 10.21136/MB.1998.126070
Classification : 53A60, 53B05
Keywords: anholonomic web; web; manifold; connection
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Vanžurová, Alena. Tensor approach to multidimensional webs. Mathematica Bohemica, Tome 123 (1998) no. 3, pp. 225-242. doi: 10.21136/MB.1998.126070

[Ak] M. A. Akivis: Three-webs of multidimensional surfaces. Trudy Geom. Sem. 2 (1969), 7-31. (In Russian.) | MR

[Ac] J. Aczél: Quasigroups, nets and nomograms. Adv. in Math. 1 (1965), 383-450. | DOI | MR

[A&S] M. A. Akivis A. M. Shelekhov: Geometry and Algebra of Multidimensional Three-Webs. Kluwer Acad. Publishers, Dordrecht, 1992. | MR

[Bo] G. Bol: Über 3-Gewebe in vierdimensionalen Raum. Math. Ann. 110 (1935), 431-463. | DOI | MR

[Ch] S. S. Chern: Eine Invariantentheorie der Dreigewebe aus r-dimensionalen Mannigfaltigkeiten im $R_{2r}$. Abh. Math. Sem. Univ. Hamburg 11 (1936), 333-358. | DOI

[Ch1] S. S. Chern: Web Geometry. Bull. AMS 6 (1982), 1-9. | MR | Zbl

[G] V. V. Goldberg: Theory of Multicodimensional (n+1)-Webs. Kluwer Acad. Publishers, Dordrecht, 1990. | MR

[Ki] M. Kikkawa: Canonical connections of homogeneous Lie loops and 3-webs. Mem. Fac. Sci. Shimane Univ. 19 (1985), 37-55. | MR | Zbl

[Ng] P. T. Nagy: Invariant tensor fields and the canonical connection of a 3-web. Aequationes Math. 35 (1988), 31-44. | DOI | MR

[Sh] I. G. Shandra: On isotranslated $n \pi$-structure and connections preserving a non-holonomic (n + 1)-coweb. Webs and Quasigroups. Tver State University, Tversk, 1995, pp. 60-66. | MR

[Va1] A. Vanžurová: On (3, 2, n)-webs. Acta Sci. Math. (Szeged) 55(1994), 657-677. | MR | Zbl

[Va2] A. Vanžurová: On torsion of a 3-web. Math. Bohem. 120 (1995), 387-392. | MR

[Va3] A. Vanžurová: Projectors of a 3-web. Proc. Conf. Dif. Geom. and Appl. Masaryk University, Brno, 1996, pp. 329-335. | MR

[Va4] A. Vanžurová: Connections for non-holonomic 3-webs. Rend. Circ. Mat. Palermo 46 (1997), 169-176. | MR

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