Dynamic Instability of Cp under Ricci Flow
نویسندگان
چکیده
The intent of this short note is to provide an independent proof of the unpublished discovery of Klaus Kröncke [Kro13] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex dimensions N ≥ 2. The unstable perturbation is not Kähler. This provides a counterexample to a well known conjecture widely attributed to Hamilton. Moreover, it shows that the expected stability of the subspace of Kähler metrics under Ricci flow, another conjecture believed by several experts, needs to be interpreted in a more nuanced way than some may have expected.
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