Geodesic
A note on the volume of $\nabla $-Einstein manifolds with skew-torsion
Communications in Mathematics, Tome 29 (2021) no. 3, pp. 385-393.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study the volume of compact Riemannian manifolds which are Einstein with respect to a metric connection with (parallel) skew\--tor\-sion. 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 \cite {Vil} related with the first variation of the volume on a compact Einstein manifold.
Classification : 53B05, 53C05, 53C25
Keywords: connections with totally skew-symmetric torsion; scalar curvature; $\nabla $-Einstein manifolds; parallel skew-torsion. 
@article{COMIM_2021__29_3_a4,
     author = {Chrysikos, Ioannis},
     title = {A note on the volume of $\nabla ${-Einstein} manifolds with skew-torsion},
     journal = {Communications in Mathematics},
     pages = {385--393},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2021},
     mrnumber = {4355412},
     zbl = {07484375},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a4/}
}
TY  - JOUR
AU  - Chrysikos, Ioannis
TI  - A note on the volume of $\nabla $-Einstein manifolds with skew-torsion
JO  - Communications in Mathematics
PY  - 2021
SP  - 385
EP  - 393
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a4/
LA  - en
ID  - COMIM_2021__29_3_a4
ER  - 
%0 Journal Article
%A Chrysikos, Ioannis
%T A note on the volume of $\nabla $-Einstein manifolds with skew-torsion
%J Communications in Mathematics
%D 2021
%P 385-393
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a4/
%G en
%F COMIM_2021__29_3_a4
Chrysikos, Ioannis. A note on the volume of $\nabla $-Einstein manifolds with skew-torsion. Communications in Mathematics, Tome 29 (2021) no. 3, pp. 385-393. http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a4/