Une caractérisation du fibré transverse

• Autores: Tong Van Duc
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 41, Fasc. 1, 1990, págs. 35-44
• Idioma: francés
• Títulos paralelos:
  • Una caracterización del fibrado transverso
• Enlaces
  • Texto completo
• Resumen

  • We prove that the Lie algebra of infinitesimal automorphisms of the transverse structure on the total space of the transverse bundle of a foliation is isomorphic to the semi-direct product of the Lie algebra of the infinitesimal automorphism of the foliation by the vector space of the transverse vector fields. The derivations of this algebra are entirely determined and we prove that this Lie algebra characterises the foliated structure of a compact Hausdorff foliation.

• Referencias bibliográficas
  • T. V. Duc, Sur la géométrie différentielle des fibrés vectoriels, Kodai Math. Sem. Report 26 (1975), 349–408.
  • T. V. Duc, Forme canonique sur le dual du fibré transverse, Ann. Fac. Sc. Toulouse 7 (1985), 169–177.
  • T. V. Duc, Tenseur covariant canonique sur le fibré cotangent d’ordre 2, Bull. Soc. Math. France (2) 110 (1986), 289–301.
  • T. V. Duc, Algèbre de Lie attachée à la structure presque-tangente, Geom. Dedicata 23 (1987), 347–352.
  • K. Fukui and N. Tomita, Lie algebra of foliation preserving vector fields, J. Math. Kyoto Univ. 22 (1983), 685–699.
  • C. S. Hsu, On a Riemannian manifold $M\_{2n}$ with an almost-tangent structure, Canad. Math. Bull. 12 (1969), 759–769.
  • A. Ichienorwicz, Algèbres de Lie attachés à un feuilletage, Ann. Fac. Sc. Toulouse 1 (1979), 45–76.
  • F. Takens, Derivations of vector fields, Comp. Math. 26 (1975), 95–99.