On the non-existence of limit E-Brody curves

TL;DR

This paper provides a straightforward proof that certain classes of complex manifolds, including ^n and (^*)^2, do not admit limit E-Brody curves, clarifying their complex geometric properties.

Contribution

It introduces a simple proof of the non-existence of limit E-Brody curves for specific manifolds using holomorphic interpolation functions.

Findings

Limit E-Brody curves do not exist for ^n and (^*)^2

The proof employs holomorphic interpolation functions

Clarifies complex structure constraints on Brody curves

Abstract

We give a simple proof of the non-existence of limit E-Brody curves, in the sense of Do Duc Thai, Mai Anh Duc and Ninh Van Thu, for a class of manifolds including $\mathbb{C}^n$ and $(\mathbb{C}^{\ast})^2$ which were studied by these authors in \cite{Do DT et al}, by constructing a suitable holomorphic interpolation function.