  Ejiri gave a negative answer to a conjecture of Lichnerowicz concerning
Riemannian manifolds with constant scalar curvature admitting an infinitesimal
non isometric conformal transformation. With this aim he constructed a warped
product of a circle of lenght $T$ and a compact manifold. But he omitted in his
analysis the condition that $T$ must to be big enough. Here we give an explicit
sharp bound $T_0 < T$ that will make the proof complete. Our presentation is
self-contained and mainly uses bifurcation techniques. Moreover, we show that
there are other such examples and contribute some results to the classification
of these manifolds.
