Perelman's entropy for some families of canonical metrics
classification
🧮 math.DG
keywords
metricsentropycanonicalmanifoldsperelmanahler-einsteinahler-ricciallows
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We numerically calculate Perelman's entropy for a variety of canonical metrics on $\mathbb{CP}^{1}$-bundles over products of Fano K\"ahler-Einstein manifolds. The metrics investigated are Einstein metrics, K\"ahler-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.
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