Rigidity Theorem for integral pinched shrinking Ricci solitons

We prove that an $n$-dimensional, $n\ge 4$, compact gradient shrinking Ricci soliton satisfying a $L^{\frac{n}{2}}$-pinching condition is isometric to a quotient of the round ${\mathbb{S}}^n$, which improves the rigidity theorem given by G. Catino (arXiv:1509.07416vl).