Reeb components of leafwise complex foliations and their symmetries II

TL;DR

This paper investigates the structure of automorphism groups of Reeb components in leafwise complex foliations, especially when boundary holonomy is infinitely tangent to the identity, revealing detailed symmetry properties.

Contribution

It provides a detailed analysis of leafwise holomorphic automorphism groups of Reeb components, extending previous work by characterizing these groups under specific boundary holonomy conditions.

Findings

Determined the structure of automorphism groups when boundary holonomy is infinitely tangent to the identity.

Identified conditions under which automorphism groups exhibit particular symmetry properties.

Extended understanding of symmetries in leafwise complex foliations with Reeb components.

Abstract

We study the group of leafwise holomorphic smooth automorphisms of Reeb components of leafwise complex foliation which are obtained by a certain Hopf construction. In particular, in the case where the boundary holonomy is infinitely tangent to the identity, we determine the structure of the group of leafwise holomorphic automorphisms.