Geodesic
Isometric immersions and embeddings of a flat M\"obius strip in Euclidean spaces
Izvestiya. Mathematics , Tome 71 (2007) no. 5, pp. 1049-1078.

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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. 
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I. Kh. Sabitov. Isometric immersions and embeddings of a flat M\"obius strip in Euclidean spaces. Izvestiya. Mathematics , Tome 71 (2007) no. 5, pp. 1049-1078. http://geodesic.mathdoc.fr/item/IM2_2007_71_5_a5/

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