2017/09/04 by Dan Knopf, Knopf, Dan, Nataša Šešum +2
Mathematics · Physics and Astronomy · #53C44 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C44
paper · pdf · doi:10.48550/arxiv.1709.01005
Corrected an error in what had been Lemma 5. Revised version to appear in The Journal of Geometric Analysis
openalex publication_date 2017/09/04 · arxiv created 2018/04/06 · arxiv updated 2018/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The intent of this short note is to provide context for and an independent proof of the discovery of Klaus Kroencke that complex projective space with its canonical Fubini--Study metric is dynamically unstable under Ricci flow in all complex dimensions N>1. The unstable perturbation is not Kaehler. This provides a counterexample to a well known conjecture widely attributed to Hamilton. Moreover, it shows that the expected stability of the subspace of Kaehler metrics under Ricci flow, another conjecture believed by several experts, needs to be interpreted in a more nuanced way than some may have expected.