{"paper":{"title":"Sasakian immersions into the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrea Loi, Beniamino Cappelletti-Montano","submitted_at":"2018-10-01T15:48:49Z","abstract_excerpt":"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 Sasak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00772","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}