FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD

Abstract

We study finite type curve in R(3)(-3) which lies in a cylinder N(2)(c). Baikousis and Blair proved that a Legendre curve in R(3)(-3) of constant curvature lies in cylinder N(2)(c) and is a 1-type curve, conversely, a 1-type Legendre curve is of constant curvature. In this paper, we will prove that a 1-type curve lying in a cylinder N(2)(c) has a constant curvature. Furthermore we will prove that a curve in R(3)(-3) which lies in a cylinder N(2)(c) is finite type if and only if the curve is 1-type.