dc.contributor.author Cleyton, Richard dc.contributor.author Moroianu, Andrei dc.contributor.author Semmelmann, Uwe dc.date.accessioned 2018-07-17T08:37:15Z dc.date.available 2018-07-17T08:37:15Z dc.date.issued 2018-07-16 dc.identifier.uri http://publications.mfo.de/handle/mfo/1376 dc.description.abstract A 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.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2018,16 dc.subject Parallel skew-symmetric torsion en_US dc.subject Nearly Kähler structures en_US dc.subject Sasakian structures en_US dc.subject Naturally reductive homogeneous spaces en_US dc.title Metric Connections with Parallel Skew-Symmetric Torsion en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2018-16 local.scientificprogram Research in Pairs 2018 en_US local.series.id OWP-2018-16 en_US local.subject.msc 53 en_US
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