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arXiv · 1909.02052

A note on the volume of $\nabla$-Einstein manifolds with skew-torsion

Ioannis Chrysikos
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Abstract

We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew-torsion. We provide a result for the sign of the first variation of the volume in terms of the corresponding scalar curvature. This generalizes a result of M. Ville, related with the first variation of the volume on a compact Einstein manifold.

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Ioannis Chrysikos. 2019-09-04. A note on the volume of $\nabla$-Einstein manifolds with skew-torsion. https://doi.org/10.2478/cm-2020-0009

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