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/