1-TYPE AND BIHARMONIC FRENET CURVES IN LORENTZIAN 3-SPACE

Abstract

type and biharmonic curves by using Laplace operator in Lorentzian 3-space are studied and some theorems and characterizations are given for these curves. E. They showed that every biharmonic curve lies in a 3-dimensional totally geodesic subspace, thus, it suffices to classify biharmonic curves in a semi-Euclidean 3-space. Inoguchi (2) pointed out that every biharmonic Frenet curve in Monkowski 3-space 3 1 E is a helix whose curvature  and torsion  satisfy 22   . In this paper we shall give the characterizations of 1-type and biharmonic curves in semi-Euclidean 3-space in terms of curvature and torsion from a different point. Firstly, we point out the general differential equation characterizing Frenet curves (both non-null and null) in a Lorentz 3-space. Moreover, we classify the special curves from the differential equations. In the final section, we give some theorems, corollaries and propositions.