Geodesic
Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type
Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 378-385.

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It is proved that a locally Euclidean metric on a circular annulus admitting an isometric immersion in $\mathbb R^2$ which is multivalued of cylindrical type can be isometrically embedded in $\mathbb R^3$ as a cylindrical surface.
Keywords: locally Euclidean metric, isometric embedding, isometric immersion, cylindrical surface, planar graph. 
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     title = {Isometric {Embeddings} in~$\mathbb{R}^3$ of an {Annulus} with a {Locally} {Euclidean} {Metric} which {Are} {Multivalued} of {Cylindrical} {Type}},
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S. N. Mikhalev; I. Kh. Sabitov. Isometric Embeddings in~$\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type. Matematičeskie zametki, Tome 98 (2015) no. 3, pp. 378-385. http://geodesic.mathdoc.fr/item/MZM_2015_98_3_a5/

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