# 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} }

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…

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