In this paper, we will give an extension of Moks theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.
In this short paper, we will give a simple and transcendental proof for Moks theorem of the generalized Frankel conjecture. This work is based on the maximum principle in cite{BS2} proposed by Brendle and Schoen.
In this paper, we proved a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.
In this paper we prove the existence of Type II singularities for the Ricci flow on $S^{n+1}$ for all $ngeq 2$.