ncts

We study automorphism groups of complex K3 surfaces in the view of hyperbolicity. After introducing the notion of (non-elementary) hyperbolicity of groups in the sense of Gromov and its importance and basic properties, we first prove that the non-elementary hyperbolicity of K3 surface automorphism depends only on the N\'eron-Severi lattices of K3 surface and gives a characterization in terms of the N\'eron-Severi lattices using recent work by Kikuta and Takatsu. We then show the finiteness of the Néron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic under the (optimal) assumption that the Picard number is greater than or equal to 6. This is a joint work with Professor Koji Fujiwara (Kyoto University) and Professor Xun Yu (Tianjing University).