Geodesic
On bounded and unbounded curves in Euclidian space
Matematičeskoe obrazovanie, no. 4 (2017), pp. 20-24 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a curve in $\mathbb{R}^3$ and provide sufficient conditions for the curve to be unbounded in terms of its curvature and torsion. We also present sufficient conditions on the curvatures for the curve to be bounded in $\mathbb{R}^4$. 
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     author = {O. \`E. Zubelevich},
     title = {On bounded and unbounded curves in {Euclidian} space},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MO_2017_4_a3/}
}
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O. È. Zubelevich. On bounded and unbounded curves in Euclidian space. Matematičeskoe obrazovanie, no. 4 (2017), pp. 20-24. http://geodesic.mathdoc.fr/item/MO_2017_4_a3/

[1] Alexander S., Bishop R., and Ghrist R., “Total curvature and simple pursuit on domains of curvature bounded above”, Geometriae Dedicata, 2010, no. 147, 275–290 | DOI | MR

[2] Courant R., Differential and Integral Calculus, v. 1, John Wiley and Sons, 1988 | MR

[3] Frenchel W., “On the differential geometry of closed space curves”, Bull. Amer. Math. Soc., 1951, no. 57, 44–54 | DOI | MR

[4] Gifford P.W., “Some refinements in theory of specialized space curves”, Amer. Math. Monthly, 1953, no. 60, 384–393 | DOI | MR

[5] Yung-Chow Wong, Hon-Fei Lai, “A Critical Examination of the Theory of Curves in Three Dimensional Differential Geometry”, Tohoku Math. Journ, 19:1 (1967) | MR