Killing and 2-Killing 1-Forms on Poisson Doubly Warped Product Manifolds

In this paper we investigate Killing and 2-Killing 1-forms on a Poisson doubly warped product manifold (PDWPM). We establish a connection between the property of 1-form on a PDWPM and its components on the factor manifolds to be Killing or 2-Killing. We also demonstrate that a Killing 1-form on a PDWPM generates a contravariant Ricci soliton factor manifold if and only if it is a contravariant Einstein manifold. Additionally, we provide necessary and sufficient conditions for a PDWPM to be a Poisson singly warped product manifold (PSWPM). Finally, we present examples of Killing and 2-Killing 1-forms on PDWPMs with one-dimensional, and two-dimensional base spaces.