Generic one-step bracket-generating distributions of rank four

Chiara De Zanet

Archivum Mathematicum (2015)

  • Volume: 051, Issue: 5, page 257-264
  • ISSN: 0044-8753

Abstract

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We give a uniform, explicit description of the generic types of one–step bracket–generating distributions of rank four. A manifold carrying such a structure has dimension at least five and no higher than ten. For each of the generic types, we give a brief description of the resulting class of generic distributions and of geometries equivalent to them. For dimensions different from eight and nine, these are available in the literature. The remaining two cases are dealt with in my doctoral thesis.

How to cite

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De Zanet, Chiara. "Generic one-step bracket-generating distributions of rank four." Archivum Mathematicum 051.5 (2015): 257-264. <http://eudml.org/doc/276104>.

@article{DeZanet2015,
abstract = {We give a uniform, explicit description of the generic types of one–step bracket–generating distributions of rank four. A manifold carrying such a structure has dimension at least five and no higher than ten. For each of the generic types, we give a brief description of the resulting class of generic distributions and of geometries equivalent to them. For dimensions different from eight and nine, these are available in the literature. The remaining two cases are dealt with in my doctoral thesis.},
author = {De Zanet, Chiara},
journal = {Archivum Mathematicum},
keywords = {generic distributions of rank four; canonical connection; parabolic geometry},
language = {eng},
number = {5},
pages = {257-264},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Generic one-step bracket-generating distributions of rank four},
url = {http://eudml.org/doc/276104},
volume = {051},
year = {2015},
}

TY - JOUR
AU - De Zanet, Chiara
TI - Generic one-step bracket-generating distributions of rank four
JO - Archivum Mathematicum
PY - 2015
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 051
IS - 5
SP - 257
EP - 264
AB - We give a uniform, explicit description of the generic types of one–step bracket–generating distributions of rank four. A manifold carrying such a structure has dimension at least five and no higher than ten. For each of the generic types, we give a brief description of the resulting class of generic distributions and of geometries equivalent to them. For dimensions different from eight and nine, these are available in the literature. The remaining two cases are dealt with in my doctoral thesis.
LA - eng
KW - generic distributions of rank four; canonical connection; parabolic geometry
UR - http://eudml.org/doc/276104
ER -

References

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  1. Agrachev, A., Marigo, A., 10.1007/s10883-005-8816-9, J. Dynam. Control System 11 (2005), 449–494. (2005) MR2170662DOI10.1007/s10883-005-8816-9
  2. Biquard, O., Quaternionic contact structures, Quaternionic contact structures in mathematics and physics (Rome 1999), Univ. Studi Roma, 1999, pp. 29–30. (1999) MR1848655
  3. Biquard, O., Métriques d’Einstein asymptotiquement symétriques, Astérisque, no. 265, Soc. Math. France Inst. Henri Poincaré, 2000. (2000) Zbl0967.53030
  4. Čap, A., Eastwood, M., Some special geometry in dimension six, Proceedings of the 22nd Winter School Geometry and Physics (Srní, 2002). Rend. Circ. Mat. Palermo (2) Suppl. No. 71, 2003, pp. 93–98. (2003) Zbl1047.53018MR1982436
  5. Čap, A., Schmalz, G., Partially integrable almost CR manifolds of CR dimension and codimension two, Lie Groups Geometric Structures and Differential Equations – One Hundred Years after Sophus Lie (KyotoNara, 1999), Adv. Stud. Pure Math. 37, 2002, electronically available as ESI Preprint 937, pp. 45–77. (2002) Zbl1041.32023MR1980896
  6. Čap, A., Slovák, J., 10.1090/surv/154, Math. Surveys Monogr., vol. 154, AMS, 2009. (2009) Zbl1183.53002MR2532439DOI10.1090/surv/154
  7. Cartan, É., Les systeme de Pfaff a cinq variables et les équations aux d érivées partielles du second ordre, Ann. Sci. École Norm. 27 (1910), 109–192. (1910) MR1509120
  8. Montgomery, R., A Tour of Subriemannian Geometries, Their Geodesics and Applications, Math. Surveys Monogr., vol. 91, AMS, 2002. (2002) Zbl1044.53022MR1867362
  9. Schmalz, G., Slovák, J., 10.4310/AJM.2000.v4.n3.a5, Asian J. Math. 4 (3) (2000), 565–598. (2000) Zbl0972.32025MR1796695DOI10.4310/AJM.2000.v4.n3.a5

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