On the Riemann-Lie algebras and Riemann-Poisson Lie groups.
Sur les intégrales premières symétriques du flot géodésique.
Spectre des laplaciens de Lichnerowicz sur les sphères et les projectifs réels.
In this paper, we compute the spectrum of the Lichnerowicz laplacian on the symmetric forms of degree 2 on the sphere S and the real projective space RP. This is obtained by generalizing to forms the calculations of the spectrum of the laplacian on fonctions done via restriction of harmonic polynomials on euclidean space.
On Riemann-Poisson Lie groups
A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in [4]. We study these Lie groups and we give a characterization of their Lie algebras. We give also a way of building these Lie algebras and we give the list of such Lie algebras up to dimension 5.
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