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This paper is devoted to the manifolds which are 4-dimensional in a complex sense and which are equipped with a holomorphic metric. Such spaces are generalizations of the 4-dimensional real manifolds, equipped with a real smooth metric. There are many advantages of the analysis of 4-dimensional complex spaces. The most important advantage is that a real smooth metric can be obtained from a complex metric by the procedure of a real slice of the complex space [8]. Moreover, the technique of a real slice leads to the real smooth metrics of different signatures. Hence, from complex spaces real Lorentzian, neutral or Riemannian spaces can be obtained1. The spaces which we analyze in this paper are two-sided conformally recurrent. Two-sided conformally recurrent spaces were defined in [5].

On Some Solutions of the Type [D] Self-dual Spaces