Communications in Mathematics |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV math/0102142 Source : ScholeXplorer IsRelatedTo DOI 10.4310/ajm.2002.v6.n2.a5 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.math/0102142
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