Geodesic
Example of a~surface that is homotopic to a~tube and has a~closed asymptotic line
Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 403-413

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The possible existence of a tube of negative Gaussian curvature with a closed asymptotic line is investigated, and an example of a closed asymptotic strip homotopic to a cylinder is formulated. 
@article{MZM_1968_3_4_a4,
     author = {G. A. Kovaleva},
     title = {Example of a~surface that is homotopic to a~tube and has a~closed asymptotic line},
     journal = {Matemati\v{c}eskie zametki},
     pages = {403--413},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a4/}
}
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G. A. Kovaleva. Example of a~surface that is homotopic to a~tube and has a~closed asymptotic line. Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 403-413. http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a4/