Tensor approach to multidimensional webs
Mathematica Bohemica (1998)
- Volume: 123, Issue: 3, page 225-242
- ISSN: 0862-7959
Access Full Article
topAbstract
topHow to cite
topVanžurová, Alena. "Tensor approach to multidimensional webs." Mathematica Bohemica 123.3 (1998): 225-242. <http://eudml.org/doc/248289>.
@article{Vanžurová1998,
abstract = {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.},
author = {Vanžurová, Alena},
journal = {Mathematica Bohemica},
keywords = {anholonomic web; web; manifold; connection; anholonomic web; web},
language = {eng},
number = {3},
pages = {225-242},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Tensor approach to multidimensional webs},
url = {http://eudml.org/doc/248289},
volume = {123},
year = {1998},
}
TY - JOUR
AU - Vanžurová, Alena
TI - Tensor approach to multidimensional webs
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 3
SP - 225
EP - 242
AB - 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.
LA - eng
KW - anholonomic web; web; manifold; connection; anholonomic web; web
UR - http://eudml.org/doc/248289
ER -
References
top- M. A. Akivis, Three-webs of multidimensional surfaces, Trudy Geom. Sem. 2 (1969), 7-31. (In Russian.) (1969) MR0254760
- J. Aczél, 10.1016/0001-8708(65)90042-3, Adv. in Math. 1 (1965), 383-450. (1965) MR0193174DOI10.1016/0001-8708(65)90042-3
- M. A. Akivis A. M. Shelekhov, Geometry and Algebra of Multidimensional Three-Webs, Kluwer Acad. Publishers, Dordrecht, 1992. (1992) MR1196908
- G. Bol, 10.1007/BF01448038, Math. Ann. 110 (1935), 431-463. (1935) MR1512949DOI10.1007/BF01448038
- S. S. Chern, 10.1007/BF02940731, Abh. Math. Sem. Univ. Hamburg 11 (1936), 333-358. (1936) DOI10.1007/BF02940731
- S. S. Chern, Web Geometry, Bull. AMS 6 (1982), 1-9. (1982) Zbl0483.53013MR0634430
- V. V. Goldberg, Theory of Multicodimensional (n+1)-Webs, Kluwer Acad. Publishers, Dordrecht, 1990. (1990) MR0998774
- M. Kikkawa, Canonical connections of homogeneous Lie loops and 3-webs, Mem. Fac. Sci. Shimane Univ. 19 (1985), 37-55. (1985) Zbl0588.53014MR0841222
- P. T. Nagy, 10.1007/BF01838155, Aequationes Math. 35 (1988), 31-44. (1988) MR0939620DOI10.1007/BF01838155
- I. G. Shandra, On isotranslated -structure and connections preserving a non-holonomic (n + 1)-coweb, Webs and Quasigroups. Tver State University, Tversk, 1995, pp. 60-66. (1995) MR1413340
- A. Vanžurová, On (3, 2, n)-webs, Acta Sci. Math. (Szeged) 55(1994), 657-677. (1994) Zbl0828.53017MR1317181
- A. Vanžurová, On torsion of a 3-web, Math. Bohem. 120 (1995), 387-392. (1995) MR1415086
- A. Vanžurová, Projectors of a 3-web, Proc. Conf. Dif. Geom. and Appl. Masaryk University, Brno, 1996, pp. 329-335. (1996) MR1406353
- A. Vanžurová, Connections for non-holonomic 3-webs, Rend. Circ. Mat. Palermo 46 (1997), 169-176. (1997) MR1469034
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.