A new 3-parameter curvature condition preserved by Ricci flow
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In this paper, we firstly establish a family of curvature invariantconditions lying between the well-known 2-nonnegative curvatureoperator and nonnegative curvature operator along the Ricci flow. Theseconditions are defined by a set of inequalities involving the first foureigenvalues of the curvature operator, which are named as 3-parameter λ-nonnegative curvature conditions. Then a related rigidity property ofmanifolds with 3-parameter λ-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the3-parameter λ-nonnegativity along Ricci flow.
Abstract
In this paper, we firstly establish a family of curvature invariantconditions lying between the well-known 2-nonnegative curvatureoperator and nonnegative curvature operator along the Ricci flow. Theseconditions are defined by a set of inequalities involving the first foureigenvalues of the curvature operator, which are named as 3-parameter λ-nonnegative curvature conditions. Then a related rigidity property ofmanifolds with 3-parameter λ-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the3-parameter λ-nonnegativity along Ricci flow.
참고문헌 (8)
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