Perelman’s Entropy for Some Families of Canonical Metrics

Abstract

We numerically calculate Perelman’s entropy for a variety of canonical metrics on -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.

2000 AMS Subject Classification::

• 53C25
• 53C44

Keywords::

• Perelman’s entropy
• Ricci flow
• Ricci Soliton
• Einstein metric