Previous |  Up |  Next


anholonomic web; web; manifold; connection
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.
[Ak] M. A. Akivis: Three-webs of multidimensional surfaces. Trudy Geom. Sem. 2 (1969), 7-31. (In Russian.) MR 0254760
[Ac] J. Aczél: Quasigroups, nets and nomograms. Adv. in Math. 1 (1965), 383-450. DOI 10.1016/0001-8708(65)90042-3 | MR 0193174
[A&S] M. A. Akivis A. M. Shelekhov: Geometry and Algebra of Multidimensional Three-Webs. Kluwer Acad. Publishers, Dordrecht, 1992. MR 1196908
[Bo] G. Bol: Über 3-Gewebe in vierdimensionalen Raum. Math. Ann. 110 (1935), 431-463. DOI 10.1007/BF01448038 | MR 1512949
[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 10.1007/BF02940731
[Ch1] S. S. Chern: Web Geometry. Bull. AMS 6 (1982), 1-9. MR 0634430 | Zbl 0483.53013
[G] V. V. Goldberg: Theory of Multicodimensional (n+1)-Webs. Kluwer Acad. Publishers, Dordrecht, 1990. MR 0998774
[Ki] M. Kikkawa: Canonical connections of homogeneous Lie loops and 3-webs. Mem. Fac. Sci. Shimane Univ. 19 (1985), 37-55. MR 0841222 | Zbl 0588.53014
[Ng] P. T. Nagy: Invariant tensor fields and the canonical connection of a 3-web. Aequationes Math. 35 (1988), 31-44. DOI 10.1007/BF01838155 | MR 0939620
[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 1413340
[Va1] A. Vanžurová: On (3, 2, n)-webs. Acta Sci. Math. (Szeged) 55(1994), 657-677. MR 1317181 | Zbl 0828.53017
[Va2] A. Vanžurová: On torsion of a 3-web. Math. Bohem. 120 (1995), 387-392. MR 1415086
[Va3] A. Vanžurová: Projectors of a 3-web. Proc. Conf. Dif. Geom. and Appl. Masaryk University, Brno, 1996, pp. 329-335. MR 1406353
[Va4] A. Vanžurová: Connections for non-holonomic 3-webs. Rend. Circ. Mat. Palermo 46 (1997), 169-176. MR 1469034
Partner of
EuDML logo