Any Sasakian structure is approximated by embeddings into spheres

Loi, Andrea;Placini, Giovanni

2024-01-01

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Abstract

We show that, for any given q >= 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 Kähler form by projectively induced ones given in [J. Ross and R. Thomas, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differential Geom. 88 2011, 1, 109-159] in the C^0-norm to a C^q-approximation.