Conformal and projective characterizations of an odd dimensional unit sphere

抄録

We obtain two characterizations of an odd-dimensional unit sphere of dimension > 3 by proving the following two results: (i) If a complete connected η-Einstein K-contact manifold M of dimension > 3 admits a conformal vector field V, then either M is isometric to a unit sphere, or V is an infinitesimal automorphism of M. (ii) If V was a projective vector field in (i), then the same conclusions would hold, except in the first case, M would be locally isometric to a unit sphere.