The main purpose of the present paper is to study almost Norden structures on 4-dimensional Walker manifolds. We discuss the integrability and Kähler (holomorphic) conditions for these structures. The curvature properties for Norden-Walker metrics is also investigated. Then examples Norden-Walker metrics are constructed from an arbitrary harmonic function of two variables.
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Salimov et al. (2010) studied this question.
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