## Ioannis Chrysikos - A note on the volume of ∇-Einstein manifolds with skew-torsion

cm:9517 - Communications in Mathematics, December 23, 2021, Volume 29 (2021), Issue 3 - https://doi.org/10.2478/cm-2020-0009
A note on the volume of ∇-Einstein manifolds with skew-torsion

Authors: Ioannis Chrysikos

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.

Volume: Volume 29 (2021), Issue 3
Published on: December 23, 2021
Imported on: May 11, 2022
Keywords: General Mathematics,[MATH]Mathematics [math]

 Source : ScholeXplorer HasVersion DOI 10.48550/arxiv.1909.02052 10.48550/arxiv.1909.02052 A note on the volume of $\nabla$-Einstein manifolds with skew-torsion Chrysikos, Ioannis ;