Rigidity of $S{U}_n$-type symmetric spaces

Abstract

We prove that the bi-invariant Einstein metric on $S{U}_{2n+1}$ is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of ${\mathbb{CP}}^{2n}\times {\mathbb{CP}}^1$ found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler--Einstein metrics on `odd' Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.

28 pages; v2 typos and small errors fixed

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