Abstract
The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold M with smooth boundary ∂M. Here, we will give the complete classification for an n-dimensional, n=3 or 4, weakly Einstein critical metric of the volume functional with nonnegative scalar curvature. Moreover, in the higher dimensional case (n≥5), we will establish a similar result for weakly Einstein critical metric under a suitable constraint on the Weyl tensor.
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