Some characterizations for Legendre curves in the 3-Dimensional Sasakian space

Abstract

In this paper, we give some characterizations for Legendre spherical, Legendre normal and Legendre rectifying curves in the 3-dimensional Sasakian space. Furthermore, we show that Legendre spherical curves are also Legendre normal curves. In particular, we prove that the inverse of curvature of a Legendre rectifying curve is a non-constant linear function of the arclength parameter.