October 2023 Almost contact structures on the set of rational curves in a 4-dimensional twistor space
Michifumi Teruya
Author Affiliations +
Kodai Math. J. 46(3): 340-370 (October 2023). DOI: 10.2996/kmj46306

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 [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].

Acknowledgment

I would like to thank my Ph.D. supervisor, Professor Nobuhiro Honda, for his useful advice on how to proceed with the research and the thesis elaboration. I would also like to thank Professor Maciej Dunajski for introducing Gundry's paper [3] to me.

Citation

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Michifumi Teruya. "Almost contact structures on the set of rational curves in a 4-dimensional twistor space." Kodai Math. J. 46 (3) 340 - 370, October 2023. https://doi.org/10.2996/kmj46306

Information

Received: 4 August 2022; Revised: 27 December 2022; Published: October 2023
First available in Project Euclid: 3 October 2023

MathSciNet: MR4649988
Digital Object Identifier: 10.2996/kmj46306

Subjects:
Primary: 53C28
Secondary: 53D15

Keywords: almost contact structure , contact metric structure , K-contact structure , Twistor theory

Rights: Copyright © 2023 Tokyo Institute of Technology, Department of Mathematics

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Vol.46 • No. 3 • October 2023
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