Geodesic
On the classification of $3$-dimensional spherical Sasakian manifolds
Izvestiya. Mathematics, Tome 85 (2021) no. 3, pp. 518-528 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we regard spherical hypersurfaces in $\mathbb{C}^2$ 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.
Keywords: geometry of Sasakian manifolds, Reeb field, Stanton surfaces. 
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D. Sykes; G. Schmalz; V. V. Ezhov. On the classification of $3$-dimensional spherical Sasakian manifolds. Izvestiya. Mathematics, Tome 85 (2021) no. 3, pp. 518-528. http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a11/

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[2] N. K. Stanton, “A normal form for rigid hypersurfaces in $\mathbf{C}^2$”, Amer. J. Math., 113:5 (1991), 877–910 | DOI | MR | Zbl

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