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

A note on the volume of ∇-Einstein manifolds with skew-torsion AbstractWe 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

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

Communications in Mathematics , Volume 29 (3): 9 – Dec 1, 2021

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Publisher
de Gruyter
Copyright
© 2021 Ioannis Chrysikos, published by Sciendo
eISSN
2336-1298
DOI
10.2478/cm-2020-0009
Publisher site
See Article on Publisher Site

Abstract

AbstractWe 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.

Journal

Communications in Mathematicsde Gruyter

Published: Dec 1, 2021

Keywords: connections with totally skew-symmetric torsion; scalar curvature; ∇ -Einstein manifolds; parallel skew-torsion; 53B05; 53C05; 53C25

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