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http://dx.doi.org/10.4134/BKMS.2010.47.6.1163

FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD  

Camci, Cetin (DEPARTMENTS OF MATHEMATICS ONSEKIZ MART UNIVERSITY)
Hacisalihoglu, H. Hilmi (DEPARTMENTS OF MATHEMATICS FACULTY OF SCIENCE BILECIK UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.6, 2010 , pp. 1163-1170 More about this Journal
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.
Keywords
Sasakian Manifold; Legendre curve; finite type curve;
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