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.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | de |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | en |
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 |
dc.identifier.urn | urn:nbn:de:101:1-2018072315521923056042 | |
dc.identifier.ppn | 165468337X | |