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

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