FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD


CAMCI Ç. , Hacisalihoglu H. H.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.47, no.6, pp.1163-1170, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 6
  • Publication Date: 2010
  • Doi Number: 10.4134/bkms.2010.47.6.1163
  • Title of Journal : BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.1163-1170

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.