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- Title
Para-Kähler-Einstein structures on Walker 4-manifolds.
- Authors
Iscan, Murat; Caglar, Gulnur
- Abstract
A 4-dimensional Walker manifold is a semi-Riemannian manifold of signature (++--) (or neutral), which admits a field of null 2-plane. The goal of this paper is to study certain almost paracomplex structures on 4-dimensional Walker manifolds. We discuss when these structures are integrable and when the para-Kähler forms are symplectic. We show that such a Walker 4-manifold can carry a class of indefinite para-Kähler-Einstein 4-manifolds, examples of indefinite para-Kähler 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.
- Subjects
EINSTEIN manifolds; INTEGRABLE functions; GOLDBACH conjecture; SYMPLECTIC manifolds; SET theory
- Publication
International Journal of Geometric Methods in Modern Physics, 2016, Vol 13, Issue 2, p-1
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887816500067