arXiv subjects

S. Yorozu

Publications and source records attributed to S. Yorozu.

2 recordsLinked to original sources

arXiv2013

Curves in R^n with finite total first curvature arising from the solutions of an ODE

We use the solution set of a real ordinary differential equation which has order n which is at least 2 to construct a smooth curve C in R^n. We describe when C is a proper embedding of infinite length with finite total first curvature.

math.DG↗

arXiv2012

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 $n$.

math.DG↗