Any Sasakian structure is approximated by embeddings into spheres

Abstract

We show that, for any given $q\geq 0$, any Sasakian structure on a closed manifold $M$ is approximated in the $C^{q}$-norm by structures induced by CR embeddings into weighted Sasakian spheres. In order to obtain this result, we also strengthen the approximation of an orbifold K\"ahler form by projectively induced ones given by Ross and Thomas in [21] in the $C^0$-norm to a $C^{q}$-approximation.