Submersion constructions for geometries with parallel skew torsion

2024/09/22 by Andrei Moroianu, Paul Schwahn, Moroianu, Andrei +1 · 1 citation
Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Structural Analysis and Optimization #Robotic Mechanisms and Dynamics

paper · pdf · doi:10.48550/arxiv.2409.14421

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 G₂-manifolds and Sasaki manifolds with reducible holonomy.

Cited by

• \mathrm G₂-structures with parallel skew-symmetric torsion

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