On a class Riemannian manifolds with harmonic Weyl conformal curvature tensor

Abstract

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