Hostname: page-component-5cf477f64f-n7lw4 Total loading time: 0 Render date: 2025-04-05T08:32:42.209Z Has data issue: false hasContentIssue false
  • English
  • Français

Une caractérisation du fibré cotangent

Published online by Cambridge University Press:  17 April 2009

Tong van Duc
Tong van Duc
Affiliation:
Laboratoire de Mathématiques, Université de Grenoble I, 38402 Saint-Martin-d'Heres, Cedex, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that the Lie algebra of infinitesimal automorphisms of the cotangent structure on the total space of the cotangent bundle of a manifold is isomorphic to the semi-direct product of the Lie algebra of the vector fields on the manifold by the space of closed 1-forms, the vector fields operating on the forms by Lie derivation. The derivations of this algebra Lie are completely determined and we prove that it characterises the cotangent bundle.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 465 - 472
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Amemia, I., ‘Lie algebra of vector fields and complex structure’, J. Math. Soc. Japan 27 (1975), 545–549.Google Scholar
[2]Clard, R.S. and Goel, R.S., ‘Almost cotangent manifolds’, J. Differential Geom. 9 (1974), 227–242.Google Scholar
[3]Duc, T.V., ‘Tenseur covenant canonique sur le fibré cotangent d'ordre 2’, Bull. Sci. Math. (2) 110 (1986), 289–301.Google Scholar
[4]Duc, T.V., ‘Algèbre de Lie attachée à la structure presque-tangente’, Geom. Dedicata 23 (1987), 347–352.Google Scholar
[5]Duc, T.V., ‘Algèbre de Lie attachée à la forme canonique sur le fibré des repères transverses’, J. Math. Pures Appl. 66 (1987), 265–271.Google Scholar
[6]Lichnerowicz, A., ‘Fibrés vectoriels, structures unimodulaires exactes et automorphismes infinitésimaux’, J. Math. Pures Appl. 56 (1977), 183–204.Google Scholar
[7]Nagano, T., ‘1-forms with the exterior derivative of maximal rang’, J. Differential Geom. 2 (1968), 251–264.CrossRefGoogle Scholar
[8]Takens, F., ‘Derivations of vector fields’, Compositio Math 28 (1973), 95–99.Google Scholar