arXiv subjects
Publications and source records attributed to Karolina Wojciechowicz.
In this paper we prove that both complete and vertical lifts of a Poisson vector field from a Poisson manifold $(M, π)$ to its tangent bundle $(TM, π_{TM})$ are also Poisson. We use this fact to describe the infinitesimal deformations of Poisson tensor $π_{TM}$. We study some of their properties and present a extensive set of examples in a low dimensional case.
We construct the family of algebroid brackets $[\cdot,\cdot]_{c,v}$ on the tangent bundle $T^*M$ to a Poisson manifold $(M,π)$ starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures on the tangent bundle $TM$. Next, in the case when $M$ is equipped with a bi-Hamiltonian structure $(M,π_1, π_2)$ we show how to construct another family of Poisson structures. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples.