Finite type curve in 3-dimensional Sasakian manifold

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CAMCI Ç., Hacisalihoglu H. H.

Bulletin of the Korean Mathematical Society, vol.47, no.6, pp.1163-1170, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 6
  • Publication Date: 2010
  • Doi Number: 10.4134/bkms.2010.47.6.1163
  • Journal Name: Bulletin of the Korean Mathematical Society
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1163-1170
  • Keywords: Finite type curve, Legendre curve, Sasakian manifold
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

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.