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http://dx.doi.org/10.4134/JKMS.2013.50.4.829

A NEW 3-PARAMETER CURVATURE CONDITION PRESERVED BY RICCI FLOW  

Gao, Xiang (School of Mathematical Sciences, Ocean University of China)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.4, 2013 , pp. 829-845 More about this Journal
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 ${\lambda}$-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;
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