Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension >= 3

Yum-Tong Siu

In this paper we prove the following theorem. Main Theorem. Let n >= 3 and m >= 3n/2 +7. Then there exists no C^m Levi-flat real hypersurface M in P_n. The condition that M is Levi…