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dc.contributor.authorCleyton, Richard
dc.contributor.authorMoroianu, Andrei
dc.contributor.authorSemmelmann, Uwe
dc.date.accessioned2018-07-17T08:37:15Z
dc.date.available2018-07-17T08:37:15Z
dc.date.issued2018-07-16
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1376
dc.description.abstractA geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing parallel skew-symmetric torsion arise naturally in several geometric contexts, e.g. on naturally reductive homogeneous spaces, nearly Kähler or nearly parallel G2-manifolds, Sasakian and 3-Sasakian manifolds, or twistor spaces over quaternion-Kähler manifolds with positive scalar curvature. In this paper we study the local structure of Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion. On every such manifold one can define a natural splitting of the tangent bundle which gives rise to a Riemannian submersion over a geometry with parallel skew-symmetric torsion of smaller dimension endowed with some extra structure. We show how previously known examples of geometries with parallel skew-symmetric torsion fit into this pattern, and construct several new examples. In the particular case where the above Riemannian submersion has the structure of a principal bundle, we give the complete local classification of the corresponding geometries with parallel skew-symmetric torsion.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2018,16
dc.subjectParallel skew-symmetric torsionen_US
dc.subjectNearly Kähler structuresen_US
dc.subjectSasakian structuresen_US
dc.subjectNaturally reductive homogeneous spacesen_US
dc.titleMetric Connections with Parallel Skew-Symmetric Torsionen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2018-16
local.scientificprogramResearch in Pairs 2018en_US
local.series.idOWP-2018-16en_US
local.subject.msc53en_US


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