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Nonexistence of Homogeneous Levi-Flat Hypersurfaces in C P 2

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  • Abdel Rahman Al-Abdallah

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

Abstract

We investigate the longstanding question of whether compact Levi-flat hypersurfaces exist in the complex projective plane CP 2 . While the nonexistence of closed real-analytic Levi-flat hypersurfaces in CP n 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 CP 2 , thus partially resolving the problem under natural symmetry assumptions.

Suggested Citation

  • Abdel Rahman Al-Abdallah, 2025. "Nonexistence of Homogeneous Levi-Flat Hypersurfaces in C P 2," Mathematics, MDPI, vol. 13(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2742-:d:1732708
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