Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Minkowski 3-space $E_1^3$

Abstract

H. K. Nickerson and Gerald S. Manning [8] derived the intrinsic equations for a relaxed elastic line on an oriented surface in the Euclidean 3-dimensional space $E^3.$ In this paper, we define a generalized relaxed elastic line and derive the intrinsic equations for a generalized of relaxed elastic line on an oriented surface in the Minkowski 3-dimensional space $E_1^3$ and give some applications of the result.