Integrable Osculating Plane Distributions

Gilcione Nonato Costa[1]

  • [1] Departamento de Matemática – ICEX – UFMG, Cep 31270-901 – Belo Horizonte, Brazil

Annales de la faculté des sciences de Toulouse Mathématiques (2013)

  • Volume: 22, Issue: 1, page 197-218
  • ISSN: 0240-2963

Abstract

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We give a necessary condition for a holomorphic vector field to induce an integrable osculating plane distribution and, using this condition, we give a characterization of such fields. We also give a generic classification for vector fields which have two invariant coordinate planes.

How to cite

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Nonato Costa, Gilcione. "Integrable Osculating Plane Distributions." Annales de la faculté des sciences de Toulouse Mathématiques 22.1 (2013): 197-218. <http://eudml.org/doc/275406>.

@article{NonatoCosta2013,
abstract = {We give a necessary condition for a holomorphic vector field to induce an integrable osculating plane distribution and, using this condition, we give a characterization of such fields. We also give a generic classification for vector fields which have two invariant coordinate planes.},
affiliation = {Departamento de Matemática – ICEX – UFMG, Cep 31270-901 – Belo Horizonte, Brazil},
author = {Nonato Costa, Gilcione},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {holomorphic vector field; osculating plane},
language = {eng},
month = {6},
number = {1},
pages = {197-218},
publisher = {Université Paul Sabatier, Toulouse},
title = {Integrable Osculating Plane Distributions},
url = {http://eudml.org/doc/275406},
volume = {22},
year = {2013},
}

TY - JOUR
AU - Nonato Costa, Gilcione
TI - Integrable Osculating Plane Distributions
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2013/6//
PB - Université Paul Sabatier, Toulouse
VL - 22
IS - 1
SP - 197
EP - 218
AB - We give a necessary condition for a holomorphic vector field to induce an integrable osculating plane distribution and, using this condition, we give a characterization of such fields. We also give a generic classification for vector fields which have two invariant coordinate planes.
LA - eng
KW - holomorphic vector field; osculating plane
UR - http://eudml.org/doc/275406
ER -

References

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  1. Bott (R.), Tu (L.W.).— Differential Forms in Algebraic Topology, Graduate Texts in Mathematics 82, Springer (1982). Zbl0496.55001MR658304
  2. Cerveau (D.).— Une liste de problèmes, Ecuaciones Diferenciales Singularidades, Universidad de Valladolid, p. 455-460 (1997). 
  3. Mol (R. S.).— Flags of holomorphic foliations, Annals of the Brazilian Academy of Science, 83(3), p. 775-786 (2011). Zbl1262.32021MR2867172
  4. Nonato Costa (G.).— Holomorphic foliations by curves on P 3 with non-isolated singularities, Annales de la Faculté des Sciences de Toulouse, S. 6, 15 no. 2, p. 297-321 (2006). Zbl1129.32018MR2244219

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