2016/07/11 by Esmail Nazari, Nazari, Esmail, Abbas Heydari +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Primary 53C15 #Secondary 53D17
paper · pdf · doi:10.48550/arxiv.1607.02907
openalex publication_date 2016/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by means of the induced Poisson structures on the integral submanifolds. Moreover, for any compatible triple with invariant metric and admissible almost complex structure, we show that the bracket annihilates on the kernel of the anchor map.