Semi-Bloch functions in several complex variables

Abstract

Let $M$ be an $n$-dimensional complex manifold. A holomorphic function $f:M\to \mathbb{C}$ is said to be semi-Bloch if for every $\hat{I}»\in \mathbb{C}$ the function $g_{\hat{I}}»=\exp (\hat{I}»f(z))$ is normal on $M$. We characterise Semi-Bloch functions on infinitesimally Kobayashi non-degenerate $M$ in geometric as well as analytic terms. Moreover, we show that on such manifolds, semi-Bloch functions are normal.