On a class of Riemannian manifolds with harmonic Weyl conformal curvature tensor

Abstract

The paper deals with the local structure of those $n$-dimensional $(n\geq 5)$ Riemannian manifolds of harmonic conformal curvature $(M,g)$ which are not conformally flat and admit a non-homothetic conformal change of metric $g \mapsto\bar g$ such that $(M,\bar g)$ is locally symmetric.