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The Journal of Geometric Analysis

, Volume 29, Issue 1, pp 902–916 | Cite as

Dynamic Instability of \(\mathbb {CP}^N\) Under Ricci Flow

  • Dan Knopf
  • Nataša Šešum
Article
  • 41 Downloads

Abstract

The intent of this short note is to provide context for and an independent proof of the discovery of Klaus Kröncke [18] that complex projective space with its canonical Fubini–Study metric is dynamically unstable under Ricci flow in all complex dimensions \(N\ge 2\). 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.

Keywords

Ricci flow Dynamic instability Complex projective space 

Mathematics Subject Classification

53C44 

Notes

Acknowledgements

Funding was provided by Division of Mathematical Sciences (Grant No. DMS-1056387).

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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  1. 1.University of Texas at AustinAustinUSA
  2. 2.Rutgers UniversityNew BrunswickUSA

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