Nonparallelism of the Ricci tensor of pseudo-cylindric metrics (Q1851078)

In the present note, the author constructs ``pseudo-cylindric'' metrics on \(S^1\times S^{n-1}\) that have harmonic curvature, but non parallel Ricci tensor. It is shown that they are conformally equivalent to a Derdzinski metric, see [\textit{A. Derdzinski}, Math. Ann. 259, 145-152 (1982; Zbl 0489.53042)]. It is also explained that a Yamabe metric on \(S^n\) with finitely many points removed has the same curvature properties.