Abstract
We prove that a Riemannian manifold admitting a metric connection with totally skew-symmetric torsion and reducible holonomy is locally reducible, provided it has nonpositive sectional curvature.
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Dileo, G., Lotta, A. A note on Riemannian connections with skew torsion and the de Rham splitting. manuscripta math. 156, 299–302 (2018). https://doi.org/10.1007/s00229-017-0967-y
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DOI: https://doi.org/10.1007/s00229-017-0967-y