Einstein manifolds of negative lower bounds on curvature operator of the second Kind

2024/11/21 by Cheng, Haiqing, Wang, Kui · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.13912

Abstract

We demonstrate that n-dimension closed Einstein manifolds, whose smallest eigenvalue of the curvature operator of the second kind of \mathringR satisfies λ₁ ≥ -θ(n) λ, are either flat or round spheres, where λ is the average of the eigenvalues of \mathringR, and θ(n) is defined as in equation (1.2). Our result improves a celebrated result (Theorem 1.1) concerning Einstein manifolds with nonnegative curvature operator of the second kind.

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