Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space \(({\mathbb {C}P}^3, g_a)\) , including nearly Kähler \({\mathbb {C}P}^3\) . Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly Kähler \({\mathbb {C}P}^3\) , 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 \({\mathbb {C}P}^3\) .
