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

Ioannis Chrysikos

Communications in Mathematics (2021)

  • Volume: 29, Issue: 3, page 385-393
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Chrysikos, Ioannis. "A note on the volume of $\nabla $-Einstein manifolds with skew-torsion." Communications in Mathematics 29.3 (2021): 385-393. <http://eudml.org/doc/298101>.

@article{Chrysikos2021,
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 [Vil] related with the first variation of the volume on a compact Einstein manifold.},
author = {Chrysikos, Ioannis},
journal = {Communications in Mathematics},
keywords = {connections with totally skew-symmetric torsion; scalar curvature; $\nabla $-Einstein manifolds; parallel skew-torsion},
language = {eng},
number = {3},
pages = {385-393},
publisher = {University of Ostrava},
title = {A note on the volume of $\nabla $-Einstein manifolds with skew-torsion},
url = {http://eudml.org/doc/298101},
volume = {29},
year = {2021},
}

TY - JOUR
AU - Chrysikos, Ioannis
TI - A note on the volume of $\nabla $-Einstein manifolds with skew-torsion
JO - Communications in Mathematics
PY - 2021
PB - University of Ostrava
VL - 29
IS - 3
SP - 385
EP - 393
AB - 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.
LA - eng
KW - connections with totally skew-symmetric torsion; scalar curvature; $\nabla $-Einstein manifolds; parallel skew-torsion
UR - http://eudml.org/doc/298101
ER -

References

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