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 $\rho (M)-2$. 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.

14 pages, important references are added. Two questions and relevant parts are moved because either they are known or solved by myself