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August 26, 2025Open Access

Nonexistence of Homogeneous Levi-Flat Hypersurfaces in CP2

Puntos clave

No homogeneous levi-flat hypersurfaces exist in CP2, resolving part of an open question.
The study combines classification methods from homogeneous CR-manifolds and projective foliation geometry.
Techniques from complex geometry were employed to tackle the longstanding issue of their existence.
This finding indicates significant restrictions on the types of structures allowed in CP2's geometry.

Resumen

We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP2. While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CPn for n>2 is well known, the case n=2 remains open. By combining techniques from the classification of homogeneous CR-manifolds with projective foliation geometry, we prove that no homogeneous Levi-flat hypersurfaces exist in CP2, thus partially resolving the problem under natural symmetry assumptions.

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Cite This Study

Abdel Rahman Al-Abdallah (Tue,) studied this question.

synapsesocial.com/papers/68af6210ad7bf08b1eae33bb https://doi.org/https://doi.org/10.3390/math13172742

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