A note on the volume of -Einstein manifolds with skew-torsion
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.