Remark on a conjecture of conformal transformations of Riemannian manifolds

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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 T₀ < 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.