The curvature center of the curves on a hypersurface in Lorentzian n-space$ L^n$

Abstract

In this paper, we define $i^{th}$ e-curvature function, $r^{th} (a_1,...,a_r)$ -curvature center and (n-r) -curvature hyperplane for the curve of Lorentzian space. We prove that the locus of centers of spheres that has p as the r-rnultiple contact point with curve is the (n-r) -curvature hyperplane in the n- dimensional Lorentzian space. We also consider some special cases. In the final section we calculate the $r^{th} (a_1,...,a_r)$ -curvature centers $C_r(t)(r = 2 or 3)$ of some special curves.