Automorphisms of hyperkähler manifolds in the view of topological entropy

Abstract

First we show that any group of automorphisms of null-entropy of a projective hyperkähler manifold $M$ is almost abelian of rank at most $ρ(M) - 2$. We then characterize automorphisms of a K3 surface with null-entropy and those with positive entropy in algebro-geometric terms. We also give an example of a group of automorphisms which is not almost abelian in each dimension.