A note on the coefficients of Rawnsley's epsilon function of Cartan-Hartogs domains

TL;DR

This paper proves that if any coefficient of Rawnsley's epsilon function for a Cartan-Hartogs domain is constant, then the domain must be biholomorphically equivalent to complex hyperbolic space, extending previous results.

Contribution

It extends previous work by showing the constancy of any coefficient implies the domain is biholomorphically equivalent to complex hyperbolic space.

Findings

Constancy of a coefficient implies the domain is hyperbolic space

Extends previous results by Feng and Tu

Provides a characterization of Cartan-Hartogs domains

Abstract

We extend a result of Z. Feng and Z. Tu by showing that if one of the coefficients $a_j$, $2\leq j\leq n$, of Rawnlsey's epsilon function associated to a $n$-dimensional Cartan-Hartogs domain is constant, then the domain is biholomorphically equivalent to the complex hyperbolic space.