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

TL;DR

This paper explores the relationship between 5-dimensional complex spacetimes with almost contact structures and 4-dimensional twistor spaces, revealing new geometric correspondences and constructions.

Contribution

It establishes a novel correspondence between certain 5D almost contact manifolds and 4D twistor spaces, including the construction of a 5D K-contact manifold from the Ren-Wang twistor space.

Findings

A correspondence between 5D almost contact manifolds and 4D twistor spaces.

Construction of a 5D K-contact manifold from the Ren-Wang twistor space.

Interpretation of the Ren-Wang twistor space within Itoh's framework.

Abstract

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, which is obtained from two copies of \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.