Riemann-Poisson manifolds and Kähler-Riemann foliations. (Q1408102)

The author studies the Kähler-Riemann foliations, as a remarkable particular case of the Riemannian foliations. The existence of a Kähler-Riemann foliation on a manifold \(P\), which is invariant (in some sense) with respect to all local foliation-preserving perpendicular vector fields, is equivalent with the existence of a regular Riemann-Poisson structure on \(P\). Finally, examples of such manifolds are provided.