Rigidity of <i>SUn</i>-Type Symmetric Spaces

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