Hypersurfaces of any homogeneous ℂP³

2025/03/11 by Liefsoens, Michaël
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.08871

Abstract

Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space (ℂP³, g_a), including nearly Kähler ℂP³. Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly Kähler ℂP³, all Hopf hypersurfaces are classified. Finally, Codazzi-like hypersurfaces (and in particular parallel and totally geodesic hypersurfaces), totally umbilical hypersurfaces and constant sectional curvature hypersurfaces are proven to not exist in any homogeneous ℂP³.

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