Semi-Bloch functions in several complex variables

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Let M be an n-dimensional complex manifold. A holomorphic function f:M→ C is said to be semi-Bloch if for every λ∈ C the function gλ=(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.