Bimeromorphic automorphism groups of non-projective hyperk\"ahler manifolds - a note inspired by C. T. McMullen

Being inspired by a work of Curtis T. McMullen about a very impressive automorphism of a K3 surface of Picard number zero, we shall clarify the structure of the bimeromorphic automorphism group of a non-projective hyperk\"ahler manifold, up to finite group factor. We also discuss relevant topics, especially, new counterexamples of Kodaira's problem about algebraic approximation of a compact K\"ahler manifold.