Bulletin of the
Korean Mathematical Society BKMS

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.

Keywords: Sasakian Manifold, Legendre curve, finite type curve

MSC numbers: Primary 53C15; Secondary 53C25