Semi-Bloch functions in several complex variables

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 $λ\in \mathbb C$ the function $g_λ=\exp(λf(z))$ 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.

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