论文标题
具有有限渐近标态曲率比的完整梯度扩展RICCI孤子
Complete gradient expanding Ricci solitons with finite asymptotic scalar curvature ratio
论文作者
论文摘要
令$（m^n，g，f）$，$ n \ geq 5 $，用非负RICCI曲率$ rc \ geq 0 $成为完整的梯度扩展Ricci Soliton。在本文中，我们表明，如果$（m^n，g，f）$的渐近标量曲率比率是有限的（即$ \ limsup_ {r \ to \ infty} r r r^2 <\ infty $） \ infty} | rm | \ \！任何$ 0 <α<2 $的r^α<\ infty $。
Let $(M^n, g, f)$, $n\geq 5$, be a complete gradient expanding Ricci soliton with nonnegative Ricci curvature $Rc\geq 0$. In this paper, we show that if the asymptotic scalar curvature ratio of $(M^n, g, f)$ is finite (i.e., $ \limsup_{r\to \infty} R r^2< \infty $), then the Riemann curvature tensor must have at least sub-quadratic decay, namely, $\limsup_{r\to \infty} |Rm| \ \! r^α< \infty$ for any $0<α<2$.
