A new curvature condition preserved by the Ricci flow

In this paper, we establish a new curvature condition preserved by the Ricci flow, which is named as 2-parameters nonnegative curvature condition. It relies on the first, second and third eigenvalues of the Riemannian curvature operator. Based on this, we prove the strong maximum principle for the 2-parameters nonnegativity along Ricci flow.