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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
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Abstract

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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

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