Local Stability of Einstein Metrics Under the Ricci Iteration

Timothy Buttsworth; Maximilien Hallgren

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arXiv · 1907.10222

Local Stability of Einstein Metrics Under the Ricci Iteration

Timothy Buttsworth·Maximilien Hallgren

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Abstract

We provide a sufficient condition for the local stability of closed Einstein manifolds of positive Ricci curvature under the Ricci iteration in terms of the spectrum of the Lichnerowicz Laplacian acting on divergence-free tensor fields. We use this result to consider the stability of several Einstein manifolds under the Ricci iteration, including symmetric spaces of compact type.

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Timothy Buttsworth, Maximilien Hallgren. 2019-07-24. Local Stability of Einstein Metrics Under the Ricci Iteration. https://arxiv.org/abs/1907.10222

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