Compact Hermitian Symmetric Spaces, Coadjoint Orbits, and the Dynamical Stability of the Ricci Flow - Hall, Stuart James; Murphy, Thomas; Waldron, James (The Journal of geometric analysis, 2021)
Using a stability criterion due to Kröncke, we show, providing n ≠ 2 k , the Kähler–Einstein metric on the Grassmannian G r k ( 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 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.