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

Haiqing Cheng; Kui Wang

Paper

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

Abstract

We demonstrate that

-dimension closed Einstein manifolds, whose smallest eigenvalue of the curvature operator of the second kind of

satisfies

, are either flat or round spheres, where

is the average of the eigenvalues of

, and

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.