On Norden-Walker 4-manifolds


A Walker 4-manifold is a semi-Riemannian manifold (M_{4} ,g) of neutral signature, which admits a field of parallel null 2-plane. The main purpose of the present paper is to study almost Norden structures on 4-dimensional Walker manifolds with respect to a proper and opposite almost complex structures. We discuss sequently the problem of integrability, Kähler (holomorphic), isotropic quasi-Kähler conditions for these structures. The curvature properties for Norden-Walker metrics is also investigated. Also, we give counterexamples to Goldberg's conjecture in the case of neutral signature.

DOI Code: 10.1285/i15900932v30n1p111

Walker 4-manifolds; Proper almost complex structure; Opposite almost complex structure; Norden metrics; Holomorphic metrics; Goldberg conjecture

Classification: 53C50; 53B30

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