An Interpolating Curvature Condition Preserved By Ricci Flow
  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. 
Xiang Gao and Yu Zheng
math.DG math.AP