Geodesic
On the Riemann-Lie Algebras and Riemann-Poisson Lie Groups
Journal of Lie theory, Tome 15 (2005) no. 1, pp. 183-195 Cet article a éte moissonné depuis la source Heldermann Verlag

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A Riemann-Lie algebra is a Lie algebra G such that its dual G* carries a Riemannian metric compatible (in the sense introduced recently by the author [C. R. Acad. Sci. Paris, S�rie I, 333 (2001) 763--768] with the canonical linear Poisson structure of G*. The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds [see Diff. Geometry Appl. 20 (2004) 279--291]. 
@article{JLT_2005_15_1_JLT_2005_15_1_a11,
     author = {M. Boucetta },
     title = {On the {Riemann-Lie} {Algebras} and {Riemann-Poisson} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {183--195},
     year = {2005},
     volume = {15},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2005_15_1_JLT_2005_15_1_a11/}
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M. Boucetta . On the Riemann-Lie Algebras and Riemann-Poisson Lie Groups. Journal of Lie theory, Tome 15 (2005) no. 1, pp. 183-195. http://geodesic.mathdoc.fr/item/JLT_2005_15_1_JLT_2005_15_1_a11/