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FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD
Camci, Cetin,Hacisalihoglu, H. Hilmi Korean Mathematical Society 2010 대한수학회보 Vol.47 No.6
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.
FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD
Cetin Camci,H. Hilmi Hacisalihoglu 대한수학회 2010 대한수학회보 Vol.47 No.6
We study finite type curve in R3(-3) which lies in a cylin-der 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, con-versely, 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.