Holonomy groups of compact flat solvmanifolds

ALEJANDRO TOLCACHIER

GEOMETRIAE DEDICATA

SPRINGER

Lugar: Berlin; Año: 2020

0046-5755

In this article we study the holonomy groups of flat solvmanifolds. It is known that the holonomy group of a flat solvmanifold is abelian; we give an elementary proof of this fact and moreover we prove that any finite abelian group is the holonomy group of a flat solvmanifold. Furthermore, we show that the minimal dimension of a flat solvmanifold with holonomy group Zn coincides with the minimal dimension of a compact flat manifold with holonomy group Zn. Finally, we give the possible holonomy groups of flat solvmanifolds in dimensions 3, 4, 5 and 6; exhibiting in the latter case a general construction to show examples of non cyclic holonomy groups.