On Walker 4-manifolds with pseudo bi-Hermitian structures

Authors : Sibel Turanli

Pages : 2299-2307

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :$\left(M_{2n},g^w,D\right)$ is a 4-dimensional Walker manifold and this triple is also a pseudo-Riemannian manifold $\left(M_{2n},g^w\right)$ of signature $(++--$) (or neutral), which is admitted a field of null 2-plane. In this paper, we consider bi-Hermitian structures $({\varphi }_1,{\ \varphi }_2)$ on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the bi-Kahler forms are symplectic.
Keywords : Almost complex structures, symplectic structures, almost Hermitian and Kahler structures, pseudobi-Hermitian structures, Walker manifold