Bulletin of the Korean Mathematical Society, vol.47, no.6, pp.1163-1170, 2010 (SCI-Expanded)
We study finite type curve in R3(-3) which lies in a cylinder N2(c). Baikousis and Blair proved that a Legendre curve in R3(-3) of constant curvature lies in cylinder N2(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 N2(c) has a constant curvature. Furthermore we will prove that a curve in R3(-3) which lies in a cylinder N2(c) is finite type if and only if the curve is 1-type. © 2010 The Korean Mathematical Society.