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Any Sasakian structure is approximated by embeddings into spheres

  • Andrea Loi and Giovanni Placini ORCID logo EMAIL logo
Published/Copyright: August 8, 2024

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.


Communicated by Shigeharu Takayama


Acknowledgements

We would to thank Julius Ross for his interest in our work and his valuable comments.

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Received: 2023-10-16
Revised: 2024-04-18
Published Online: 2024-08-08
Published in Print: 2025-06-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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