# Metric connections with parallel skew-symmetric torsion

@article{Cleyton2018MetricCW, title={Metric connections with parallel skew-symmetric torsion}, author={Richard Cleyton and Andrei Moroianu and Uwe Semmelmann}, journal={arXiv: Differential Geometry}, year={2018} }

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 Kahler or nearly parallel $\mathrm{G}_2$-manifolds, Sasakian and $3$-Sasakian manifolds, or twistor spaces over quaternion-Kahler manifolds…

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