Remark on a conjecture of conformal transformations of Riemannian manifolds
Abstract
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.