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In this paper, we provide a correspondence between certain 5-dimensionalcomplex spacetimes and 4-dimensional twistor spaces. The spacetimes are almostcontact manifolds whose curvature tensor satisfies certain conditions. By usingthe correspondence, we show that a 5-dimensional K-contact manifold can beobtained from the Ren-Wang twistor space, which is obtained from two copies of\C^4 identifying open subsets by a holomorphic map. From this result, theRen-Wang twistor space can be interpreted in the framework of Itoh.

Almost contact structures on the set of rational curves in a 4-dimensional twistor space