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arXiv · 2503.08871

Hypersurfaces of any homogeneous $\mathbb{C}P^3$

Michaël Liefsoens
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Abstract

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

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Michaël Liefsoens. 2025-03-11. Hypersurfaces of any homogeneous $\mathbb{C}P^3$. https://arxiv.org/abs/2503.08871

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