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A NEW 3-PARAMETER CURVATURE CONDITION PRESERVED BY RICCI FLOW

  • Gao, Xiang (School of Mathematical Sciences, Ocean University of China)
  • Received : 2011.09.09
  • Published : 2013.07.01

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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