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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Product twistor spaces and Weyl geometry

Author: Johann Davidov
Journal: Proc. Amer. Math. Soc. 148 (2020), 3491-3506
MSC (2010): Primary 53C28; Secondary 53C15, 53D18
Published electronically: May 11, 2020
Uncorrected version: Original version posted May 11, 2020
Corrected version: This paper was corrected and reposted due to a misunderstanding between the publisher and the author.
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Abstract: Motivated by generalized geometry (à la Hitchin), we discuss the integrability conditions for four natural almost complex structures on the product bundle $ \mathcal {Z}\times \mathcal {Z}\to M$, where $ \mathcal {Z}$ is the twistor space of a Riemannian 4-manifold $ M$ endowed with a metric connection $ D$ with skew-symmetric torsion. These structures are defined by means of the connection $ D$ and four (Kähler) complex structures on the fibres of this bundle. Their integrability conditions are interpreted in terms of Weyl geometry, and this is used to supply examples satisfying the conditions.

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Additional Information

Johann Davidov
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G.Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria

Keywords: Twistor spaces, almost complex structures, skew-symmetric torsion, Weyl geometry
Received by editor(s): February 11, 2019
Received by editor(s) in revised form: May 15, 2019
Published electronically: May 11, 2020
Additional Notes: The author was partially supported by the National Science Fund, Ministry of Education and Science of Bulgaria under contract DN 12/2
Dedicated: Dedicated to the memory of Thomas Friedrich
Communicated by: Jia-Ping Wang
Article copyright: © Copyright 2020 American Mathematical Society