| 王林峰.加权Ricci流的非拟周期性[J].数学年刊A辑,2009,30(4):467~478 |
| 加权Ricci流的非拟周期性 |
| No Breathers About the Weighted Ricci Flow |
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| DOI： |
| 中文关键词: 加权Ricci流 拟周期性 熵 |
| 英文关键词:Weighted Ricci flow, Breather, Entropy |
| 基金项目:国家自然科学基金，江苏省高校自然科学基础研究面上项目，南通大学自然科学基金，南通大学博士科研基金(No.08804)资助的项目 |
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| 中文摘要: |
| (M,g)是n维黎曼流形,h是M上的光滑函数,相应的加权测度为dμ(x)=eh(x)dV(x),m维Bakry-Emery曲率张量为Ricm,考虑了加权Ricci流(a)g/(a)t=-2Ricm,当流形是紧致时,排除了加权Ricci流的拟周期性,推广了紧致流形上Ricci流的相应结果. |
| 英文摘要: |
| Let $(M, g)$ be an $n$-dimensional
Riemannian manifold, $h$ a smooth function on
$M$, $\mathrm{d}\mu(x)=\rme^{h(x)}\mathrm{d}V(x)$ the weighted measure
and $\mathrm{Ric}_m$ the $m$-dimensional Bakry-Emery curvature
tensor. This paper considers the weighted Ricci flow $\frac{\partial
g}{\partial t}=-2\mathrm{Ric}_m$ and rules out breathers
about this flow when the manifold is compact, which generalizes the
same result about Ricci flow on compact manifold. |
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