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Submersion constructions for geometries with parallel skew torsion
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Submersion constructions for geometries with parallel skew torsion
abstract
In the absence of a de Rham decomposition theorem for geometries with torsion, we develop and unify ways to view a geometry with parallel skew torsion as the total space of a locally defined, not necessarily unique Riemannian submersion with totally geodesic fibers. We complete and extend the Cleyton-Swann classification of irreducible such geometries and characterize the cases where the stabilizer of the torsion is larger than the holonomy. As a byproduct, we obtain structure results on Gray manifolds, nearly parallel G$_2$-manifolds and Sasaki manifolds with reducible holonomy.
Forward citations
Cited by 2 Pith papers
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Classification of 7D Riemannian manifolds with parallel skew-symmetric torsion and G2-holonomy, up to naturally reductive spaces and nearly parallel G2-structures, extending Friedrich's cocalibrated work.
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