Some Local Expressions of Special Curves in Three Dimentional Finsler Manifold F3

Abstract

In the Euclidean space E³, there exist three classes of curves, so-called rectifying, normal and osculating curves satisfying the planes spanned by {T, B}, {N, B} and {T, N} as well as to each unit speed curve  I [ IR ->E³ whose orthogonal unit vector fields T, N, B called respectively the tangent, the principal normal and the binormal vector fields. In this paper, we give the definition of rectifying, normal and osculating curves in 3-dimensional Finsler manifold. Furthermore, we obtain some characterizations related to these curves.