• Corpus ID: 119630136

Sasakian immersions into the sphere

@article{CappellettiMontano2018SasakianII,
  title={Sasakian immersions into the sphere},
  author={Beniamino Cappelletti-Montano and Andrea Loi},
  journal={arXiv: Differential Geometry},
  year={2018}
}

• Beniamino Cappelletti-Montano, A. Loi
• Published 1 October 2018
• Mathematics
• arXiv: Differential Geometry

The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and $\eta$-Einstein cases when the codimension of the immersion is $4$. Moreover, we exhibit infinite families of compact Sasakian $\eta$--Einstein manifolds which cannot admit a Sasakian immersion into any odd-dimensional sphere. Finally, we show that, after possibly performing a ${\mathcal {D}}$-homothetic deformation, a homogeneous Sasakian manifold can be Sasakian immersed into some odd-dimensional sphere if and only if $S$ is regular and either $S$ is simply--connected or its fundamental group is finite cyclic.