Finiteness of the total first curvature of a non-closed curve in $\mathbb{E}^{n}$

Autor:	Kim, C. Y., Matsuda, H., Park, J. H., Yorozu, S.
Rok vydání:	2012
Předmět:	Mathematics - Differential Geometry 53A04
Druh dokumentu:	Working Paper
Popis:	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 $n$. Comment: 22 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1211.3844 Zobrazit plný text záznamu View this record from Arxiv