Simply connectedness of gradient Shrinking Ricci solitons

Absos Ali Shaikh, Chandan Kumar Mondal

Published 2020-02-06Version 1

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 simply connected. 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.