A note on the volume of-Einstein manifolds with skew-Torsion

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 [15] related with the first variation of the volume on a compact Einstein manifold. © 2021 Ioannis Chrysikos, published by Sciendo.