On the classification of 3-dimensional spherical Sasakian manifolds

Daniel Sykes, Gerd Schmalz, Vladimir V. Ezhov

Research output: Contribution to journalArticlepeer-review


In this article we regard spherical hypersurfaces in C2 with a fixed Reeb vector field as 3-dimensional Sasakian manifolds. We establish a correspondence between three different sets of parameters, namely, those arising from representing the Reeb vector field as an automorphism of the Heisenberg sphere, those used in Stanton's description of rigid spheres, and those arising from the rigid normal forms. We also describe geometrically the moduli space for rigid spheres and provide a geometric distinction between Stanton hypersurfaces and those found in [1]. Finally, we determine the Sasakian automorphism groups of rigid spheres and detect the homogeneous Sasakian manifolds among them.
Original languageEnglish
Pages (from-to)518-528
Number of pages11
JournalIzvestiya Mathematics
Issue number3
Publication statusPublished - Jun 2021


  • Geometry of Sasakian manifolds
  • Reeb field
  • Stanton surfaces


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