We investigate the curvature operator of the second kind on Riemannian manifolds and
prove several classification results. The first one asserts that a closed Riemannian manifold …

We show that an n-dimensional Riemannian manifold with n-nonnegative or n-nonpositive
curvature operator of the second kind has restricted holonomy SO (n) or is flat. The result …

We show that a closed four-manifold with 4 1 2-positive curvature operator of the second
kind is diffeomorphic to a spherical space form. The curvature assumption is sharp as both …

We investigate the curvature operator of the second kind on product Riemannian manifolds
and obtain some optimal rigidity results. For instance, we prove that the universal cover of an …

This article aims to investigate the curvature operator of the second kind on Kähler
manifolds. The first result states that an m-dimensional Kähler manifold with 3 2 (m 2-1) …

We investigate Riemannian manifolds $(M^ n, g) $ whose curvature operator of the second
kind $\mathring {R} $ satisfies the condition\begin {equation*}\alpha …

We demonstrate that $ n $-dimension closed Einstein manifolds, whose smallest eigenvalue
of the curvature operator of the second kind of $\mathring {R} $ satisfies $\lambda_1\ge …

This article aims to understand the behavior of the curvature operator of the second kind
under the Ricci flow in dimension three. First, we express the eigenvalues of the curvature …