Hartogs-Bochner type theorem in projective space

Abstract

We prove the following Hartogs-Bochner type theorem: Let $M$ be a connected $C^2$ hypersurface of $P_n(\mathbb{C})$ ($n\ge 2$) which divides $P_n(\mathbb{C})$ in two connected open sets ${\Omega }_1$ and ${\Omega }_2$. Then there exists $i\in \{1,2\}$ such that $C^1$ CR functions defined on $M$ extends holomorphically to ${\Omega }_i$.

arXiv comment23 pages, version with minor corrections