Isometric Embeddings in $\mathbb{R}^3$ of an Annulus with a Locally Euclidean Metric which Are Multivalued of Cylindrical Type

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.