Para-Kahler-Einstein structures on Walker 4-manifolds
MetadataShow full item record
CitationIscan, M., & Caglar, G. (2016). Para-Kähler–Einstein structures on Walker 4-manifolds. International Journal of Geometric Methods in Modern Physics, 13(02), 1650006.
A 4-dimensional Walker manifold (M-4, g, D) is a semi-Riemannian manifold (M-4, g) of signature (+ + --) (or neutral), which admits a field of null 2-plane. The goal of this paper is to study certain almost paracomplex structures phi on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the para Kahler forms are symplectic. We show that such a Walker 4-manifold can carry a class of indefinite para-Kahler-Einstein 4-manifolds, examples of indefinite para-Kahler 4-manifolds, and also almost indefinite para-Hermitian-Einstein 4-manifold. Finally, we give a counterexample for the almost para-Hemitian version of Goldberg conjecture.