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

2022/06/27 by Michifumi Teruya, Teruya, M.
Mathematics · Physics and Astronomy · #53C28(Primary) #53D15(Secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2206.13151

openalex publication_date 2022/06/27 · openalex created_date 2022/06/30 · openalex updated_date 2026/07/28

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 \C⁴ identifying open subsets by a holomorphic map. From this result, the Ren-Wang twistor space can be interpreted in the framework of Itoh.

Related

• Contact twistor spaces and almost contact metric structures
• From complex contact structures to real almost contact 3-structures
• Compatible Complex Structures on Twistor Spaces
• Product twistor spaces and Weyl geometry
• Curvature properties of the Chern connection of twistor spaces