Finiteness of the total first curvature of a non-closed curve in   $\mathbb{E}^{n}$
  We consider a regular smooth curve in $\mathbb{E}^n$ such that its coordinates' components are the fundamental solutions of the differential equation $ y^{(n)} (x) - y(x) = 0 ,$ $x \in \mathbb{R} $ of order $n$. We show that the total first curvature of this curve is infinite for odd $n$ and is finite for even $n$. 
C. Y. Kim, H. Matsuda, J. H. Park, and S. Yorozu
math.DG