Publication details
A note on the volume of Nabla-Einstein manifolds with skew-torsion
| Authors | |
|---|---|
| Year of publication | 2021 |
| Type | Article in Periodical |
| Magazine / Source | Communications in Mathematics |
| Citation | |
| Web | http://eudml.org/doc/298101 |
| Doi | http://dx.doi.org/10.2478/cm-2020-0009 |
| Keywords | connections with totally skew-symmetric torsion; scalar curvature; nabla-Einstein manifolds; parallel skew-torsion |
| Description | 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 [Vil] related with the first variation of the volume on a compact Einstein manifold. |