Isometric immersions and embeddings of a flat Möbius strip in Euclidean spaces

We establish formulae for isometric embeddings and immersions of Möbius bands with a locally Euclidean metric and study extrinsic geometric properties of these surfaces. We consider both standard Möbius bands corresponding to embeddings of a rectangular Möbius strip and general Möbius bands, in particular, those with generators orthogonal to the directrix.