On the Sharpness of One Integral Inequality for Closed Curves in ?SUP4/SUP

摘要

The sharpness of the integral inequality Rγpk21 + k22 + k23ds 2π forclosed curves with nowhere vanishing curvatures in R4is discussed. Weprove that an arbitrary closed curve of constant positive curvatures in R4satisfies the inequality Rγpk21 + k22 + k23ds ≥ 2√5π.