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

In this paper, we provide a correspondence between certain 5-dimensional complex spacetimes and 4-dimensional twistor spaces. The spacetimes are almost contact manifolds whose curvature tensor satisfies certain conditions. By using the correspondence, we show that a 5-dimensional K-contact manifold can be obtained from the Ren-Wang twistor space [10], which is obtained from two copies of $\mathbb{C}^4$ identifying open subsets by a holomorphic map. From this result, the Ren-Wang twistor space can be interpreted in the framework of Itoh [5].