The Second Main Theorem for spherically symmetric K\"ahler manifolds

TL;DR

This paper extends the classical Second Main Theorem to spherically symmetric Kähler manifolds, analyzing the value distribution of holomorphic maps within this geometric context.

Contribution

It establishes a Second Main Theorem for a new class of Kähler manifolds, broadening the scope of value distribution theory in complex geometry.

Findings

Second Main Theorem analogous to classical cases

Applicable to spherically symmetric Kähler manifolds

Enhances understanding of holomorphic map value distribution

Abstract

We investigate the value distribution of holomorphic maps defined on one class of K\"ahler manifolds. With the very natural settings, we establish a Second Main Theorem which is of the similar form as ones of the classical Second Main Theorem for complex Euclidean spaces and complex unit balls.