Locally Sasakian Manifolds

Abstract

We show that every Sasakian manifold in dimension $2k+1$ is locally generated by a free real function of $2k$ variables. This function is a Sasakian analogue of the K\"ahler potential for K\"ahler geometry. It is also shown that every locally Sasakian-Einstein manifold in $2k+1$ dimensions is generated by a locally K\"ahler-Einstein manifold in dimension $2k$.