Linearization of transition functions along a certain class of Levi-flat hypersurfaces

TL;DR

This paper develops a normal form for transition functions on certain Levi-flat hypersurfaces using circle dynamics and linearization techniques, providing a geometric analogue of Arnol'd's theorem.

Contribution

It introduces a new normal form for transition functions on Levi-flat hypersurfaces via suspension and linearization methods, extending Arnol'd's linearization theorem.

Findings

Established a sufficient condition for linearization of transition functions.

Connected geometric structures of Levi-flat hypersurfaces with circle dynamics.

Provided a framework for normal forms in complex geometry.

Abstract

We pose a normal form of transition functions along some Levi-flat hypersurfaces obtained by suspension. By focusing on methods in circle dynamics and linearization theorems, we give a sufficient condition to obtain a normal form as a geometrical analogue of Arnol'd's linearization theorem.