Curvature properties of the Chern connection of twistor spaces

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dc.creatorDavidov, J.
dc.creatorGrantcharov, G.
dc.creatorMuskarov, O.
dc.date2005-03-18
dc.date.accessioned2026-07-07T05:18:07Z
dc.date.available2026-07-07T05:18:07Z
dc.descriptionThe twistor space \Z of an oriented Riemannian 4-manifold M admits a natural 1-parameter family of Riemannian metrics h_t compatible with the almost complex structures J_1 and J_2 introduced, respectively, by Atiyah, Hitchin and Singer, and Eells and Salamon. In this paper we compute the first Chern form of the almost Hermitian manifold (\Z,h_t,J_n), n=1,2 and find the geometric conditions on M under which the curvature of its Chern connection D^n is of type (1,1). We also describe the twistor spaces of constant holomorphic sectional curvature with respect to D^n and show that the Nijenhuis tensor of J_2 is D^2-parallel provided the base manifold M is Einstein and self-dual.
dc.description14 pages, to appear in Rocky Mountain J. Math
dc.identifierhttps://arxiv.org/abs/math/0503384
dc.identifierhttp://arxiv.org/abs/math/0503384
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74547
dc.subjectDifferential Geometry
dc.subject53C15
dc.titleCurvature properties of the Chern connection of twistor spaces
dc.typetext

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