On Normal Forms for Levi-flat hypersurfaces with an Isolated Line Singularity

TL;DR

This paper establishes normal forms for certain Levi-flat hypersurfaces with isolated line singularities and provides conditions under which such hypersurfaces are pullbacks of real-analytic curves via holomorphic functions.

Contribution

It introduces new normal form results for Levi-flat hypersurfaces with line singularities and characterizes when they are pullbacks of real-analytic curves.

Findings

Normal forms for Levi-flat hypersurfaces with isolated line singularities.

Conditions for hypersurfaces to be pullbacks of real-analytic curves.

Characterization of singularities in Levi-flat hypersurfaces.

Abstract

We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for that a Levi-flat hypersurface with a complex line as singularity to be a pullback of a real-analytic curve in C via a holomorphic function.