On Walker 4-manifolds with pseudo bi-Hermitian structures

Abstract

$(M_{2n,}g^omega,D)$ is a 4-dimensional Walker manifold and this triple is also a pseudo-Riemannian manifold $(M_{2n,}g^omega)$ of signature (+ + −−) (or neutral), which is admitted a field of null 2-plane. In this paper, we considerbi-Hermitian structures $(rho_{1,};rho_2)$ on 4-dimensional Walker manifolds. We discuss when these structures are integrableand when the bi-Kähler forms are symplectic.