An Interpolating Curvature Condition Preserved By Ricci Flow

Details An Interpolating Curvature Condition Preserved By Ricci Flow An Interpolating Curvature Condition Preserved By Ricci Flow

2011-05-26

arxiv.org/abs/1105.5311v2

Mathematics

Differential Geometry

Scientific paper

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.

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