Manifolds with harmonic Weyl curvature and curvature operator of the second kind

Fuente: arXiv
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Main Authors: Fu, Haiping, Lu, Yao
Format: Preprint
Published: 2026
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author Fu, Haiping
Lu, Yao
author_facet Fu, Haiping
Lu, Yao
contents We prove that a compact Riemannian manifold of dimension $n\ge 8$ with harmonic Weyl curvature and $\frac{3(n-1)(n+2)}{4(3n-1)}$-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}.
format Preprint
id arxiv_https___arxiv_org_abs_2602_07313
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Manifolds with harmonic Weyl curvature and curvature operator of the second kind
Fu, Haiping
Lu, Yao
Differential Geometry
We prove that a compact Riemannian manifold of dimension $n\ge 8$ with harmonic Weyl curvature and $\frac{3(n-1)(n+2)}{4(3n-1)}$-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}.
title Manifolds with harmonic Weyl curvature and curvature operator of the second kind
topic Differential Geometry
url https://arxiv.org/abs/2602.07313