The Second main theorem of holomorphic maps on spherically symmetric Kähler manifolds
Abstract
Spherically symmetric manifolds are one class of important Riemannian models in mathematics and physics which includes the most common spaces such as Euclidean spaces, balls and spheres, etc.. In this paper, we consider the Nevanlinna theory concerning value distribution of holomorphic maps from a spherically symmetric Kähler manifold into a complex projective manifold under the assumption that the dimension of sources is not less than one of targets. In our settings, a Second Main Theorem is obtained, which extends the classical Second Main Theorem of holomorphic maps defined on $\mathbb C^m$ and $\mathbb B^m_{\mathbb C}.$ In particular, one extends the CarlsonGriffiths' equidistribution theory of holomorphic maps from $\mathbb C^m$ into complex projective manifolds. When some curvature condition is satisfied, we derive a defect relation of Nevanlinna theory.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.13874
 Bibcode:
 2021arXiv211013874D
 Keywords:

 Mathematics  Complex Variables;
 32H30