## Generalized Hantzsche-Wendt flat manifolds.(English)Zbl 1159.53328

Summary: We study the family of closed Riemannian $$n$$-manifolds with holonomy group isomorphic to $$\mathbb{Z}_2^{n-1}$$, which we call generalized Hantzsche-Wendt manifolds. We prove results on their structure, compute some invariants, and find relations between them, illustrated in a graph connecting the family.

### MSC:

 53C29 Issues of holonomy in differential geometry 20H15 Other geometric groups, including crystallographic groups 57N16 Geometric structures on manifolds of high or arbitrary dimension 57S30 Discontinuous groups of transformations 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)

### Keywords:

flat manifold; Bieberbach group; holonomy representation
Full Text:

### Online Encyclopedia of Integer Sequences:

Number of generalized Hantzsche-Wendt manifolds in dimension n.

### References:

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