An Interpolating Curvature Condition Preserved By Ricci Flow

Abstract

In this paper, we firstly establish an Interpolating curvature invariance between the well known nonnegative and 2-non-negative curvature invariant along the Ricci flow. Then a related strong maximum principle for the $({\lambda }_1,{\lambda }_2)$-nonnegativity is also derived along Ricci flow. Based on these, finally we obtain a rigidity property of manifolds with $({\lambda }_1,{\lambda }_2)$-nonnegative curvature operators.