  A formal treatment of Killing 1-form and 2-Killing 1-form on Riemannian
Poisson manifold, Riemannian Poisson warped product space are presented. In
this way, we obtain Bochner type result on compact Riemannian Poisson manifold,
compact Riemannian Poisson warped product space for Killing 1-form and
2-Killing 1-form. Finally, we give the characterization of a 2-Killing 1-form
on $(\mathbb{R}^2,g,\Pi)$.
