On the geometry of compatible Poisson and Riemannian structures

Abstract

We consider compatibility conditions between Poisson and Riemannian structures on smooth manifolds by means of a contravariant partially complex structure, or $f$-structure, introducing the notion of (almost) Kähler--Poisson manifolds. In addition, we study some of their properties under structure preserving maps and symmetries.

References in corpus (1)

• Killing-Poisson tensors on Riemannian manifolds