CONFORMAL MOTION OF CONTACT MANIFOLDS WITH CHARACTERISTIC VECTOR FIELD IN THE k-NULLITY DISTRIBUTION

摘要

It is known (see for example, [17]) that if an m-dimensional Riemannian manifold admits a maximal, i.e., an (m + 1)(m + 2)/2-parameter group of conformal motions, then it is conformally flat. It is also known that a conformally flat Sasakian (normal contact metric) manifold is of constant curvature 1. This shows that the existence of maximal conformal group places a severe restriction on the Sasakian manifold. Thus one is led to examine the effect of the existence of a single 1-parameter group of conformal motions on a Sasakian manifold. All the transformations considered in this paper are infinitesimal.