Geodesic
On the sharpness of one integral inequality for closed curves in $\mathbb R^4$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 4, pp. 502-509 
Vasyl Gorkavyy; Raisa Posylaieva. On the sharpness of one integral inequality for closed curves in $\mathbb R^4$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 4, pp. 502-509. http://geodesic.mathdoc.fr/item/JMAG_2019_15_4_a2/
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     title = {On the sharpness of one integral inequality for closed curves in $\mathbb R^4$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The sharpness of the integral inequality $\int_\gamma\sqrt{k_1^2+k_2^2+k_3^2} ds>2\pi$ for closed curves with nowhere vanishing curvatures in $\mathbb R^4$ is discussed. We prove that an arbitrary closed curve of constant positive curvatures in $\mathbb R^4$ satisfies the inequality $\int_\gamma\sqrt{k_1^2+k_2^2+k_3^2} ds\geq 2\sqrt{5}\pi$.

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