Intrinsic equations for a relaxed elastic line on an oriented hypersurface in the Minkowski space $Bbb{R}^n_1$

Abstract

We gived the intrinsic equations for a relaxed elastic line on an oriented surface In this paper, we derived the intrinsic equations for a relaxed elastic line on an oriented time-like hypersurface and space-like hypersurface in the Minkowski space $Bbb{R}^n_1$ and gived additional results about relaxed elastic lines on various timelike and spacelike hypersurface in the Minkowski space $Bbb{R}^n_1$.