Normal holomorphic curves from parabolic regions to projective spaces

TL;DR

This paper surveys known results and introduces new theorems about normal holomorphic curves from parabolic regions to complex projective spaces, focusing on their properties and classifications.

Contribution

It provides a comprehensive survey and presents new theorems on the behavior and characteristics of normal holomorphic curves into projective spaces.

Findings

Summary of existing results on normal holomorphic curves

New theorems characterizing such curves

Insights into the structure of Brody curves

Abstract

A holomorphic map from the complex line to a complex projective space is called normal (a. k. a. Brody curve) if it is uniformly continuous from the Euclidean metric to the Fubini--Study metric. The paper contains a survey of known results about such maps, as well as some new theorems.