Nonexistence of Homogeneous Levi-Flat Hypersurfaces in C P 2

Abdel Rahman Al-Abdallah ()
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Abdel Rahman Al-Abdallah: Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada

Mathematics, 2025, vol. 13, issue 17, 1-13

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.

Keywords: Levi-flat hypersurfaces; complex projective plane ( C P 2 ); homogeneous CR manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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