2014/01/02 by Mohamed Boucetta, Boucetta, Mohamed, Zouhair Saassai +1
Mathematics · Physics and Astronomy · #53D17 #58B34 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #math.DG #msc:53D17 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1401.0477
19 pages
arxiv created 2014/01/02 · openalex publication_date 2014/01/02 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (M,π,D) be a Poisson manifold endowed with a flat, torsion-free contravariant connection. We show that if D is an F-connection then there exists a tensor T such that DT is the metacurvature tensor introduced by E. Hawkins in his work on noncommutative deformations. We compute T and the metacurvature tensor in this case, and show that if T=0 then, near any regular point, π and D are defined in a natural way by a Lie algebra action and a solution of the classical Yang-Baxter equation. Moreover, when D is the contravariant Levi-Civita connection associated to π and a Riemannian metric, the Lie algebra action preserves the metric.