Higher Dimensional M\"obius Bands and Their Boundaries

TL;DR

This paper characterizes Bieberbach manifolds that serve as geodesic boundaries of compact flat manifolds, focusing on low-dimensional cases up to dimension 4, providing insights into their geometric structure.

Contribution

It offers a new characterization of certain Bieberbach manifolds as boundaries of flat manifolds, especially in low dimensions, expanding understanding of their geometric properties.

Findings

Characterization of Bieberbach manifolds as geodesic boundaries

Analysis of low-dimensional cases up to dimension 4

Insights into the structure of flat manifolds and their boundaries

Abstract

We give a characterisation of Bieberbach manifolds which are geodesic boundaries of a compact flat manifold, and discuss the low dimensional cases, up to dimension 4.