On Fenchel's problem
Matematičeskie zametki, Tome 56 (1994) no. 5, pp. 87-97.

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Yu. A. Nikolaevskii. On Fenchel's problem. Matematičeskie zametki, Tome 56 (1994) no. 5, pp. 87-97. http://geodesic.mathdoc.fr/item/MZM_1994_56_5_a7/

[1] Fenchel W., “On the differential geometry of closed space curves”, Bull. Amer. Math. Soc., 57:1 (1951), 44–54 | DOI | MR | Zbl

[2] Cheng-chung H., “A differential-geometric criterion for a space curve to be closed”, Proc. Amer. Math. Soc., 83:2 (1981), 359–361 | DOI

[3] Aminov Yu. A., “Ob usloviyakh zamknutosti lomanykh linii i mnogogrannikov v $E^3$”, Matem. zametki, 38:1 (1985), 132–141 | MR | Zbl

[4] Aminov Yu. A., “O zamknutykh krivykh – trigonometricheskikh polinomakh dliny dugi”, Issledovaniya po geometrii “v tselom” i matematicheskomu analizu, Trudy Instituta Matematiki AN SSSR, 9, Nauka. Sib. otd., Novosibirsk, 1987, 25–34 | MR | Zbl

[5] Nikolaevskii Yu. A., “O probleme V. Fenkhelya”, Mezhdun. nauch. konf. “Lobachevskii i sovremennaya geometriya”, Tezisy dokladov. Ch. 1, Kazan, 1992, 68