Journal of the mathematical society of japan vol:61 issue:2 pages:363-377
Using a criterion of Johnson-Rees  we give a list of all four and six dimensional flat Kahler manifolds. We calculate their R-cohomology, including the Hodge numbers. As a corollary; we classify all flat complex manifolds of dimension 3 whose holonomy groups are subgroups of SU(3). Moreover, we define a family of flat Kahler manifolds which are generalizations of tire oriented Hantzsche-Wendt Riemannian manifolds .