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June 2020 On the normalized Ricci flow with scalar curvature converging to constant
Chanyoung Sung
Kodai Math. J. 43(2): 268-277 (June 2020). DOI: 10.2996/kmj/1594313554

Abstract

We show that the normalized Ricci flow $g(t)$ on a smooth closed manifold $M$ existing for all $t \geq 0$ with scalar curvature converging to constant in $L^2$ norm should satisfy $$\liminf_{t\rightarrow \infty} \int_M|\stackrel{\circ}{r}|_{g(t)}^2d\mu_{g(t)} =0,$$ where $\stackrel{\circ}{r}$ is the trace-free part of Ricci tensor. Using this, we give topological obstructions to the existence of such a Ricci flow (even with positive scalar curvature tending to $\infty$ in sup norm) on 4-manifolds.

Citation

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Chanyoung Sung. "On the normalized Ricci flow with scalar curvature converging to constant." Kodai Math. J. 43 (2) 268 - 277, June 2020. https://doi.org/10.2996/kmj/1594313554

Information

Published: June 2020
First available in Project Euclid: 9 July 2020

zbMATH: 07227750
MathSciNet: MR4121363
Digital Object Identifier: 10.2996/kmj/1594313554

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 2 • June 2020
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