On the automorphism groups of models in $\mathbb C^2$

TL;DR

This paper characterizes models in complex two-dimensional space by their automorphism groups and provides explicit descriptions of these groups, enhancing understanding of their structure and symmetries.

Contribution

It offers a new characterization of models in ^2 based on their automorphism groups and explicitly describes these groups, which was not previously known.

Findings

Models in ^2 are characterized by their noncompact automorphism groups

Explicit descriptions of automorphism groups of models in ^2 are provided

The results deepen understanding of symmetries in complex two-dimensional models

Abstract

In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for automorphism groups of models in $\mathbb C^2$.