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On the stability of Einstein manifolds

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Abstract

Certain curvature conditions for the stability of Einstein manifolds with respect to the Einstein–Hilbert action are given. These conditions are given in terms of quantities involving the Weyl tensor and the Bochner tensor. In dimension six, a stability criterion involving the Euler characteristic is given.

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Acknowledgments

This article is based on a part of the authors’ PhD-thesis. The author would like to thank his advisor Christian Bär for helpful discussions. Moreover, the author thanks the Max-Planck Institute for Gravitational Physics for financial support.

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Correspondence to Klaus Kröncke.

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Kröncke, K. On the stability of Einstein manifolds. Ann Glob Anal Geom 47, 81–98 (2015). https://doi.org/10.1007/s10455-014-9436-y

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  • DOI: https://doi.org/10.1007/s10455-014-9436-y

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