Hypersurfaces of any homogeneous $\mathbb{C}P^3$
Differential Geometry
2025-03-13 v1
Abstract
Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space , including nearly K\"ahler . Notably, all extrinsically homogeneous hypersurfaces are classified in all these spaces, with an explicit family of examples. Moreover, for nearly K\"ahler , 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 .
Cite
@article{arxiv.2503.08871,
title = {Hypersurfaces of any homogeneous $\mathbb{C}P^3$},
author = {Michaël Liefsoens},
journal= {arXiv preprint arXiv:2503.08871},
year = {2025}
}