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arXiv · 2009.05259

A property of the spherical derivative of an entire curve in complex projective space

Nguyen Thanh Son·Tran Van Tan
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Abstract

We establish a type of the Picard's theorem for entire curves in $P^n(\mathbb C)$ whose spherical derivative vanishes on the inverse images of hypersurface targets. Then, as a corollary, we prove that there is an union $D$ of finite number of hypersurfaces in the complex projective space $P^n(\mathbb C)$ such that for every entire curve $f$ in $P^n(\mathbb C)$, if the spherical derivative $f^{\#}$ of $f$ is bounded on $ f^{-1}(D)$, then $f^{\#}$ is bounded on the entire complex plane, and hence, $f$ is a Brody curve.

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Nguyen Thanh Son, Tran Van Tan. 2020-09-11. A property of the spherical derivative of an entire curve in complex projective space. https://arxiv.org/abs/2009.05259

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