We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set and that each element of is represented by a manifold with finite holonomy group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-28, author = {Micha\l\ Sadowski}, title = {Holonomy groups of complete flat manifolds}, journal = {Banach Center Publications}, volume = {75}, year = {2007}, pages = {527-532}, zbl = {1122.53028}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-28} }
Michał Sadowski. Holonomy groups of complete flat manifolds. Banach Center Publications, Tome 75 (2007) pp. 527-532. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-28/