Spherical CR-symmetric hypersurfaces in Hermitian symmetric spaces (Q6183823)

This paper studies the classification of spherical symmetric CR manifolds. \textit{G. Dileo} and \textit{A. Lotta} [Bull. Aust. Math. Soc. 80, No. 2, 251--274 (2009; Zbl 1204.53038)] gave a classification of spherical symmetric CR manifolds. In this paper, the authors refine the previous classification. More precisely, they use that the first author [Ann. Mat. Pura Appl. (4) 199, No. 5, 1873--1884 (2020; Zbl 1446.53045)] obtained a complete classification of non-Sasakian CR-symmetric manifolds and realized them as real hypersurfaces in Hermitian symmetric spaces, and that \textit{A. Carriazo}, the first author and \textit{V. Martín-Molina} [``Generalized Sasakian Space Forms Which Are Realized as Real Hypersurfaces in Complex Space Forms'', Mathematics 8 (2020), No. 6, 873] gave a classification of Sasakian space form real hypersurfaces of constant \(\phi\)-sectional curvature \(H_{0}=c+1\). The authors match these two classifications with Dileo and Lotta's result and then realize spherical symmetric CR manifolds as real hypersurfaces in Hermitian symmetric spaces. The authors also give a characterization of locally pseudo-Hermitian symmetric contact strongly pseudo-convex CR space forms, reducing them to Sasakian \(\phi\)-symmetric spaces and non-Sasakian contact \((k,\mu)\)-spaces. Combining it with the classifications above, they also establish classification theorems for locally pseudo-Hermitian symmetric CR space forms of higher dimensions and of dimension 3.