Sphere Theorems for $\frac{10}{3}$-Positive Curvature Operator of the Second Kind

In this paper, we prove that every connected closed Riemannian manifold of dimension $n\geq4$ with $\frac{10}{3}$-positive curvature operator of the second kind is diffeomorphic to a spherical space form. We also obtain a classification of connected closed Riemannian manifolds with $\frac{10}{3}$-no