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- W1993434162 abstract "Soit ( M, g ) une variété riemannienne. Nous montrons que l'espace vectoriel G des formes symétriques invariantes par le flot géodésique est une algèbre de Lie contenant (comme sous-algèbre) l'algèbre des champs de Killing ainsi que l'espace vectoriel des formes symétriques parallèles comme sous-algèbre abélienne. Dans un deuxième temps, nous donnons une décomposition de Weitzenböck d'un certain laplacien sur les formes symétriques et en déduisons une généralisation d'un théorème de S. Bochner [2]. Let (M, g) be a Riemannian manifold. We prove that the space of symmetric tensors invariant under the geodesic flow, is a Lie algebra which contains, as a subalgebra, the Lie algebra of Killing vector fields, and which also contains the space of parallel symmetric tensors as an Abelian subalgebra. Morever, we give a Weitzenböck decomposition of some Laplace—Beltrami operator on symmetric tensors and prove a vanishing theorem which generalizes a theorem due to S. Bochner [2]." @default.
- W1993434162 created "2016-06-24" @default.
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- W1993434162 date "1998-06-01" @default.
- W1993434162 modified "2023-09-24" @default.
- W1993434162 title "Courbure sectiounelle et intégrales premières symétriques du flot géodésique: généralisation d'un théorème de S. Bochner" @default.
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- W1993434162 doi "https://doi.org/10.1016/s0764-4442(98)80400-x" @default.
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