Using a stability criterion due to Kröncke, we show, providing \({n\ne 2k}\), the Kähler–Einstein metric on the Grassmannian \(Gr_{k}(\mathbb {C}^{n})\) of complex k-planes in an n-dimensional complex vector space is dynamically unstable as a fixed point of the Ricci flow. This generalises the recent results of Kröncke and Knopf–Sesum on the instability of the Fubini–Study metric on \(\mathbb {CP}^{n}\) for \(n>1\). The key to the proof is using the description of Grassmannians as certain coadjoint orbits of SU(n). We are also able to prove that Kröncke’s method will not work on any of the other compact, irreducible, Hermitian symmetric spaces.

我们使用基于Kröncke的稳定性判据，提供了\（{n \ ne 2k} \），即Grassmannian \（Gr_ {k}（\ mathbb {C} ^ {n}）\）上的Kähler-Einstein度量作为Ricci流的固定点，n维复矢量空间中的复k平面的运动是动态不稳定的。这归纳了Kröncke和Knopf–Sesum最近关于\（\ mathbb {CP} ^ {n} \）对\（n> 1 \）的Fubini-Study度量的不稳定性的最新结果。证明的关键是使用格拉斯曼学说作为SU（n）。我们还能够证明Kröncke的方法不适用于其他任何紧凑的，不可约的Hermitian对称空间。