Stable and unstable Einstein warped products

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 $n\ge 10$.

26 pages, published version

References in corpus (3)

• Stability and instability of Ricci solitons
• Dynamical stability and instability of Ricci-flat metrics
• On infinitesimal Einstein deformations

Cited by in corpus (4)

• Stability of Ricci de Turck flow on Singular Spaces
• Spectra, rigidity and stability of sine-cones
• Local and global scalar curvature rigidity of Einstein manifolds
• Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow