Estimates on the non-compact expanding gradient Ricci solitons
Estimates on the non-compact expanding gradient Ricci solitons
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DOI：
10.2478/auom-2013-0046
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
Xiang Gao;Qiaofang Xing;R. Cao
中科院分区：
文献类型：
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作者：
Xiang Gao;Qiaofang Xing;R. Cao
摘要本文讨论了具有正Ricci曲率的完全非紧膨胀梯度Ricci孤子（Mn,g）。在Ricci曲率为正且标量曲率趋近于0的条件下，我们得到了势函数增长的一个有用估计。在此基础上，在相同的假设条件下，证明了∫t0 Rc (γ′（s), γ′(s)）ds和∫t0 Rc （γ′（,s））。v)ds至少有线性增长，其中7(5)是最小法向测地线，从R得到最大值的点出发。此外，还得到了关于Ricci曲率的其他一些结果。
Abstract In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫t0 Rc (γ'(s) , γ' (s))ds and ∫t0 Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained.