Let M be a (compact) smooth manifold. What kind of obstruction exist for M to admit a metric whose Ricci flow is a t-periodic flow?
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asked Jul 31, 2023 at 14:05
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6$\begingroup$ Doesn't Perelman's entropy formula rule out periodic flows that are not stationary? $\endgroup$– Willie WongCommented Jul 31, 2023 at 14:34
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$\begingroup$ @WillieWong Thank you for your comment and Prelman work. I was not aware of Perelman work. $\endgroup$– Ali TaghaviCommented Jul 31, 2023 at 14:40
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$\begingroup$ @WillieWong The only thing I had already heard was "Prelman solved Poincare conjecture via Ricci flow" Then I serach for definition of Ricci flow I realized it is a 1 parameter family of metric with certain differential equation. So I posed the question when is this 1 parameter periodic. I was some how inspired by obstructions for manifold to be an Einstein manifold. I thank you again for informing me of the Entropy formula. $\endgroup$– Ali TaghaviCommented Jul 31, 2023 at 15:05
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