Perelman's entropy for some families of canonical metrics

Abstract

We numerically calculate Perelman's entropy for a variety of canonical metrics on ${\mathbb{CP}}^1$-bundles over products of Fano Kähler-Einstein manifolds. The metrics investigated are Einstein metrics, Kähler-Ricci solitons and quasi-Einstein metrics. The calculation of the entropy allows a rough picture of how the Ricci flow behaves on each of the manifolds in question.

11 pages, to appear in Experimental Mathematics

References in corpus (2)

• Gaussian densities and stability for some Ricci solitons
• Quasi-Einstein metrics on hypersurface families