Geodesic
On the sharpness of one integral inequality for closed curves in $\mathbb R^4$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019), pp. 502-509

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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 $\int_\gamma\sqrt{k_1^2+k_2^2+k_3^2} ds\geq 2\sqrt{5}\pi$. 
@article{JMAG_2019_15_a2,
     author = {Vasyl Gorkavyy and Raisa Posylaieva},
     title = {On the sharpness of one integral inequality for closed curves in $\mathbb R^4$},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {502--509},
     publisher = {mathdoc},
     volume = {15},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2019_15_a2/}
}
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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), pp. 502-509. http://geodesic.mathdoc.fr/item/JMAG_2019_15_a2/