On Riemannian Poisson warped product space

TL;DR

This paper explores the properties of Killing and 2-Killing 1-forms on Riemannian Poisson manifolds and warped product spaces, deriving Bochner-type results and characterizations.

Contribution

It provides a formal framework for Killing forms on Riemannian Poisson spaces and extends Bochner-type theorems to these structures, including a specific characterization on .

Findings

Bochner type results established for compact Riemannian Poisson manifolds

Characterization of 2-Killing 1-form on  with specific metric and Poisson structure

Formal treatment of Killing forms on Riemannian Poisson warped product spaces

Abstract

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 $(\mathbb{R}^2,g,\Pi)$.