Geodesic
Metacurvature of Riemannian Poisson-Lie Groups
Journal of Lie theory, Tome 19 (2009) no. 3, pp. 439-462 Cet article a éte moissonné depuis la source Heldermann Verlag

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We study the triple (G, π, .,.> ) where G is a connected and simply connected Lie group, π and .,.> are, respectively, a multiplicative Poisson tensor and a left invariant Riemannian metric on G such that the necessary conditions, introduced by Hawkins, to the existence of a non commutative deformation (in the direction of π) of the spectral triple associated to .,.> are satisfied. We show that the geometric problem of the classification of such triples (G, π, .,.> ) is equivalent to an algebraic one. We solve this algebraic problem in low dimensions and we give a list of all triples (G, π, .,.> ) satisfying Hawkins's conditions, up to dimension four.
Classification : 58B34, 46I65, 53D17
Mots-clés : Poisson-Lie groups, contravariant connections, metacurvature, spectral triple 
@article{JLT_2009_19_3_JLT_2009_19_3_a0,
     author = {A. Bahayou and M. Boucetta },
     title = {Metacurvature of {Riemannian} {Poisson-Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {439--462},
     year = {2009},
     volume = {19},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2009_19_3_JLT_2009_19_3_a0/}
}
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A. Bahayou; M. Boucetta . Metacurvature of Riemannian Poisson-Lie Groups. Journal of Lie theory, Tome 19 (2009) no. 3, pp. 439-462. http://geodesic.mathdoc.fr/item/JLT_2009_19_3_JLT_2009_19_3_a0/