A note on the volume of ∇-Einstein manifolds with skew-torsion-Reference-Cited by-同舟云学术

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

Published:2021-12-01 Issue:3 Volume:29 Page:385-393
ISSN:2336-1298
Container-title:Communications in Mathematics
language:en
Short-container-title:

Author:

Chrysikos Ioannis¹

Affiliation:

1. University of Hradec Králové , Faculty of Science , Rokitanského 62, 500 03 Hradec Králové, Czech Republic

Abstract

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 [15] related with the first variation of the volume on a compact Einstein manifold.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/cm-2020-0009

Reference15 articles.

1. [1] I. Agricola, A.C. Ferreira: Einstein manifolds with skew torsion. Oxford Quart. J. (65) (2014) 717–741.

2. [2] I. Agricola, Th. Friedrich: On the holonomy of connections with skew-symmetric torsion. Math. Ann. (328) (2004) 711–748.

3. [3] I. Agricola, J. Becker-Bender, H. Kim: Twistorial eigenvalue estimates for generalized Dirac operators with torsion. Adv. Math. (243) (2013) 296–329.

4. [4] B. Ammann, C. Bär: The Einstein-Hilbert action as a spectral action. Noncommutative Geometry and the Standard Model of Elementary Particle Physics (2002) 75–108.

5. [5] A.L. Besse: Einstein manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag (1987).

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