Reeb components of leafwise complex foliations and their symmetries III

TL;DR

This paper computes the automorphism groups of 3D Reeb components with complex leaves, specifically those constructed via the Hopf construction with non-tangent boundary holonomy, advancing understanding of their symmetries.

Contribution

It provides a detailed computation of automorphism groups for a class of 3D Reeb components, extending previous work and offering a near-complete classification.

Findings

Automorphism groups are explicitly computed for Hopf-constructed Reeb components.

The work covers cases with boundary holonomy not tangent to the identity.

Results contribute to the classification of leafwise holomorphic automorphisms.

Abstract

The automorphisms group of the 3-dimensional Reeb component with complex leaves is computed in the case where the component is obtained by the Hopf construction and the holonomy of the boundary leaf is not tangent to the identity to the infinite order. Combined with a previous work, for 3-dimensional Reeb components obtained by the Hopf construction, we have an almost complete description of the groups of leafwise holomorphic smooth automorphisms.