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Transactions of the American Mathematical Society

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Stable and unstable Einstein warped products

Author: Klaus Kröncke
Journal: Trans. Amer. Math. Soc. 369 (2017), 6537-6563
MSC (2010): Primary 58J05, 53C25, 53C21
Published electronically: May 16, 2017
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Abstract: In this article, we systematically investigate the stability properties of certain warped product Einstein manifolds. We characterize stability of these metrics in terms of an eigenvalue condition of the Einstein operator on the base manifold. In particular, we prove that all complete manifolds carrying imaginary Killing spinors are strictly stable. Moreover, we show that Ricci-flat and hyperbolic cones over Kähler-Einstein Fano manifolds and over nonnegatively curved Einstein manifolds are stable if the cone has dimension $ n\geq 10$.

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Additional Information

Klaus Kröncke
Affiliation: Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany

Keywords: Einstein metrics, linear stability, Ricci-flat cones, hyperbolic cones
Received by editor(s): September 14, 2015
Received by editor(s) in revised form: April 13, 2016
Published electronically: May 16, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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