Manifolds with harmonic Weyl curvature and curvature operator of the second kind
Differential Geometry
2026-02-10 v1
Abstract
We prove that a compact Riemannian manifold of dimension with harmonic Weyl curvature and -nonnegative curvature operator of the second kind is either globally conformally equivalent to a space of positive constant curvature or is isometric to a flat manifold. In particular, We also give a classification of four-dimensional manifolds with harmonic Weyl curvature satisfying a cone condition. This result generalizes the work in \cite{DFY24,FLD,Li22}.
Keywords
Cite
@article{arxiv.2602.07313,
title = {Manifolds with harmonic Weyl curvature and curvature operator of the second kind},
author = {Haiping Fu and Yao Lu},
journal= {arXiv preprint arXiv:2602.07313},
year = {2026}
}