A NEW 3-PARAMETER CURVATURE CONDITION PRESERVED BY RICCI FLOW

Title & Authors
A NEW 3-PARAMETER CURVATURE CONDITION PRESERVED BY RICCI FLOW
Gao, Xiang;

Abstract
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 $\small{{\lambda}}$-nonnegative curvature conditions. Then a related rigidity property of manifolds with 3-parameter $\small{{\lambda}}$-nonnegative curvature operators is also derived. Based on these, we also obtain a strong maximum principle for the 3-parameter $\small{{\lambda}}$-nonnegativity along Ricci flow.
Keywords
Ricci flow;3-parameter $\small{{\lambda}}$-nonnegative curvature operator;maximum principle;
Language
English
Cited by
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