EXAMPLES OF EINSTEIN MANIFOLDS WITH ALL POSSIBLE HOLONOMY GROUPS IN DIMENSIONS LESS-THAN 7

In an earlier work, the possible holonomy groups of all compact locally irreducible Riemannian manifolds of dimensions up to ten were classified, placing particular emphasis on the non-simply-connected case. In this work, the problem of finding examples of manifolds with such holonomy groups is discussed. It is proven, in particular, that it is possible to find (Einsteinian) examples of every one of the 23 holonomy types corresponding to manifolds of dimensions less than 7: Thus, an exact characterization of the groups that can occur as holonomy groups can be given in those dimensions.