Tensor approach to multidimensional webs

Alena Vanžurová

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 3, page 225-242
  • ISSN: 0862-7959

Abstract

top
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.

How to cite

top

Vanžurová, 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
  1. M. A. Akivis, Three-webs of multidimensional surfaces, Trudy Geom. Sem. 2 (1969), 7-31. (In Russian.) (1969) MR0254760
  2. J. Aczél, 10.1016/0001-8708(65)90042-3, Adv. in Math. 1 (1965), 383-450. (1965) MR0193174DOI10.1016/0001-8708(65)90042-3
  3. M. A. Akivis A. M. Shelekhov, Geometry and Algebra of Multidimensional Three-Webs, Kluwer Acad. Publishers, Dordrecht, 1992. (1992) MR1196908
  4. G. Bol, 10.1007/BF01448038, Math. Ann. 110 (1935), 431-463. (1935) MR1512949DOI10.1007/BF01448038
  5. S. S. Chern, 10.1007/BF02940731, Abh. Math. Sem. Univ. Hamburg 11 (1936), 333-358. (1936) DOI10.1007/BF02940731
  6. S. S. Chern, Web Geometry, Bull. AMS 6 (1982), 1-9. (1982) Zbl0483.53013MR0634430
  7. V. V. Goldberg, Theory of Multicodimensional (n+1)-Webs, Kluwer Acad. Publishers, Dordrecht, 1990. (1990) MR0998774
  8. M. Kikkawa, Canonical connections of homogeneous Lie loops and 3-webs, Mem. Fac. Sci. Shimane Univ. 19 (1985), 37-55. (1985) Zbl0588.53014MR0841222
  9. P. T. Nagy, 10.1007/BF01838155, Aequationes Math. 35 (1988), 31-44. (1988) MR0939620DOI10.1007/BF01838155
  10. I. G. Shandra, On isotranslated n π -structure and connections preserving a non-holonomic (n + 1)-coweb, Webs and Quasigroups. Tver State University, Tversk, 1995, pp. 60-66. (1995) MR1413340
  11. A. Vanžurová, On (3, 2, n)-webs, Acta Sci. Math. (Szeged) 55(1994), 657-677. (1994) Zbl0828.53017MR1317181
  12. A. Vanžurová, On torsion of a 3-web, Math. Bohem. 120 (1995), 387-392. (1995) MR1415086
  13. A. Vanžurová, Projectors of a 3-web, Proc. Conf. Dif. Geom. and Appl. Masaryk University, Brno, 1996, pp. 329-335. (1996) MR1406353
  14. A. Vanžurová, Connections for non-holonomic 3-webs, Rend. Circ. Mat. Palermo 46 (1997), 169-176. (1997) MR1469034

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.