FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD

Title & Authors
FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD
Camci, Cetin; Hacisalihoglu, H. Hilmi;

Abstract
We study finite type curve in $\small{R^3}$(-3) which lies in a cylinder $\small{N^2}$(c). Baikousis and Blair proved that a Legendre curve in $\small{R^3}$(-3) of constant curvature lies in cylinder $\small{N^2}$(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 $\small{N^2}$(c) has a constant curvature. Furthermore we will prove that a curve in $\small{R^3}$(-3) which lies in a cylinder $\small{N^2}$(c) is finite type if and only if the curve is 1-type.
Keywords
Sasakian Manifold;Legendre curve;finite type curve;
Language
English
Cited by
1.
On ruled surface in 3-dimensional almost contact metric manifold, International Journal of Geometric Methods in Modern Physics, 2017, 14, 05, 1750076
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