İşcan, MuratÇağlar, Gülnur2021-09-132021-09-132016Iscan, M., & Caglar, G. (2016). Para-Kähler–Einstein structures on Walker 4-manifolds. International Journal of Geometric Methods in Modern Physics, 13(02), 1650006.https://doi.org/10.1142/S0219887816500067https://hdl.handle.net/11494/3418A 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.eninfo:eu-repo/semantics/closedAccessAlmost paracomplex structureSymplectic structurePara-Kahler structureEinstein metricWalker manifoldArticle13210.1142/S0219887816500067Q2N/A