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Isometry theorem of gradient Shrinking Ricci solitons
Journal of Geometry and Physics ( IF 1.5 ) Pub Date : 2021-01-11 , DOI: 10.1016/j.geomphys.2021.104110
Absos Ali Shaikh , Chandan Kumar Mondal

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 shown that a four dimensional gradient shrinking Ricci soliton satisfying some conditions is isometric to S4 or RP4 or CP2. We have also deduced a condition for the shrinking Ricci soliton to be compact with quadratic volume growth.



中文翻译:

梯度收缩里奇孤子的等距定理

在本文中,我们证明了,如果完全保形的平坦梯度收缩的Ricci孤子具有线性体积增长,或者标量曲率是有限可积的,并且势函数的倒数是次谐波的,那么流形对欧几里得球是等距的。结果,我们证明了满足某些条件的四维梯度收缩的Ricci孤子与小号4 要么 RP4 要么 CP2。我们还推论出了利氏孤子不断缩小并随二次体积增长而压缩的条件。

更新日期:2021-01-24
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