Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2009.03.11
  • Published : 2010.11.30
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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.

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References

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