Abstract

We consider relations between two families of flat manifolds with holonomy group Z2 of diagonal type: the family RBM of real Bott manifolds and the family GHW of generalized Hantzsche-Wendt manifolds. In particular, we prove that the intersection GHW∩RBM is not empty. Moreover, we consider some class of real Bott manifolds without Spin and SpinC structure. There are given conditions (Theorem 1) for the existence of such structures. As an application a list of all 5-dimensional oriented real Bott manifolds without Spin structure is given.

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