A note on the volume of $\nabla$-Einstein manifolds with skew-torsion
Differential Geometry
2020-09-15 v1
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.
Keywords
Cite
@article{arxiv.1909.02052,
title = {A note on the volume of $\nabla$-Einstein manifolds with skew-torsion},
author = {Ioannis Chrysikos},
journal= {arXiv preprint arXiv:1909.02052},
year = {2020}
}
Comments
7 pages, to appear in "Communications in Mathematics"