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Mathematics > Differential Geometry

arXiv:2206.13151 (math)
[Submitted on 27 Jun 2022 (v1), last revised 26 Dec 2022 (this version, v3)]

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

Authors:M. Teruya
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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.
Comments: 37 pages with 2figures
Subjects: Differential Geometry (math.DG)
MSC classes: 53C28(Primary), 53D15(Secondary)
Cite as: arXiv:2206.13151 [math.DG]
  (or arXiv:2206.13151v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2206.13151

Submission history

From: Michifumi Teruya [view email]
[v1] Mon, 27 Jun 2022 09:55:52 UTC (25 KB)
[v2] Thu, 28 Jul 2022 02:49:37 UTC (26 KB)
[v3] Mon, 26 Dec 2022 13:06:26 UTC (28 KB)
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