Levi-flats in $\mathbb{CP}^n$: a survey for nonexperts

TL;DR

This survey introduces nonexperts to the topic of Levi-flat hypersurfaces in complex projective spaces, focusing on their nonexistence proofs and related results for dimensions greater than two.

Contribution

It compiles and explains various proofs of nonexistence of real analytic Levi-flat hypersurfaces in higher-dimensional complex projective spaces, making the topic accessible to nonexperts.

Findings

Nonexistence of real analytic Levi-flat hypersurfaces in $\

$ ext{CP}^n$ for $n>2$ is established through multiple proofs.

Generalizations and related results are discussed.

Abstract

This survey paper, aimed at nonexperts in the field, explores various proofs of nonexistence of real analytic Levi-flat hypersurfaces in $\mathbb CP^n$, $n>2$. Some generalizations and other related results are also discussed.