SU(3)-structures on submanifolds of a Spin(7)-manifold

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dc.creatorIvanov, Stefan
dc.creatorCabrera, Francisco Martín
dc.date2005-10-19
dc.date2007-06-28
dc.date.accessioned2026-07-07T11:44:15Z
dc.date.available2026-07-07T11:44:15Z
dc.descriptionLocal SU(3)-structures on an oriented submanifold of Spin(7)-manifold are determined and their types are characterized in terms of the shape operator and the type of the Spin(7)-structure. An application to Bryant \cite{MR89b:53084} and Calabi \cite{MR24 #A558} examples is given. It is shown that the product of a Cayley plane and a minimal surface lying in a four-dimensional orthogonal Cayley plane with the induced complex structure from the octonions described by Bryant in \cite{MR89b:53084} admits a holomorphic local complex volume form exactly when it lies in a three-plane, i.e. it coincides with the example constructed by Calabi in \cite{MR24 #A558}. In this case the holomorphic (3,0)-form is parallel with respect to the unique Hermitian connection with totally skew-symmetric torsion.
dc.description25 pages, no figures, some improvements and clarifications are made, final version to appear in Diff. Geom. Appl
dc.identifierhttps://arxiv.org/abs/math/0510406
dc.identifierhttp://arxiv.org/abs/math/0510406
dc.identifierDiff.Geom.Appl.26:113-132,2008
dc.identifierdoi:10.1016/j.difgeo.2007.11.006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201535
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subject53C15, 53C26
dc.titleSU(3)-structures on submanifolds of a Spin(7)-manifold
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