论文标题
梯度缩小的Ricci孤子的等轴测定理
Isometry theorem of gradient Shrinking Ricci solitons
论文作者
论文摘要
在本文中，我们已经证明，如果完全扁平的梯度收缩Ricci Soliton具有线性体积的生长，或者标量曲率是有限整合的，并且潜在函数的相互谐波也是亚谐波，那么该歧管对欧几里得球体等均等。结果，我们已经表明，满足某些条件的四维梯度收缩ricci soliton与$ \ mathbb {s}^4 $或$ \ Mathbb {rp}^4 $或$ \ MATHBB {CP {CP}^2 $。我们还推导了缩小的Ricci Soliton的条件，使其具有二次体积增长。
In this paper, we have proved that if a complete conformally flat gradient shrinking Ricci soliton has linear volume growth or the scalar curvature is finitely integrable and also the reciprocal of the potential function is subharmonic, then the manifold is isometric to the Euclidean sphere. As a consequence, we have showed that a four dimensional gradient shrinking Ricci soliton satisfying some conditions is isometric to $\mathbb{S}^4$ or $\mathbb{RP}^4$ or $\mathbb{CP}^2$. We have also deduced a condition for the shrinking Ricci soliton to be compact with quadratic volume growth.
