Stable and unstable Einstein warped products

Kröncke, Klaus

doi:10.1090/tran/6959

Stable and unstable Einstein warped products
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by Klaus Kröncke PDF

Trans. Amer. Math. Soc. 369 (2017), 6537-6563 Request permission

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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