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arXiv · 1402.5625

Perelman's entropy for some families of canonical metrics

Stuart James Hall
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Abstract

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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Stuart James Hall. 2014-02-23. Perelman's entropy for some families of canonical metrics. https://arxiv.org/abs/1402.5625

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