Journal of the
Korean Mathematical Society JKMS

In this paper, we firstly establish a family of curvature invariant conditions lying between the well-known 2-nonnegative curvature operator and nonnegative curvature operator along the Ricci flow. These conditions are defined by a set of inequalities involving the first four eigenvalues of the curvature operator, which are named as 3-parameter $\lambda $-nonnegative curvature conditions. Then a related rigidity property of manifolds with 3-parameter $\lambda $-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the 3-parameter $\lambda $-nonnegativity along Ricci flow.

Keywords: Ricci flow, 3-parameter $\lambda $-nonnegative curvature operator, maximum principle

MSC numbers: 58G25, 35P05