Automorphisms and examples of compact non-Kähler manifolds - Magnússon, Gunnar Þór (MATHEMATICA SCANDINAVICA, 2017)
If $f$ is an automorphism of a compact simply connected Kähler manifold with trivial canonical bundle that fixes a Kähler class, then the order of $f$ is finite. We apply this well known result to construct compact non-Kähler manifolds. These manifolds contradict the abundance and Iitaka conjectures for complex manifolds.