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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.
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참고문헌 (8)
참고문헌 신청
B. Y. Chen / 1990 / Curves of finite type, Geometry and topology of submanifolds, Ⅱ / World Sci. Publ. : 76 ~ 110
C. Baikoussis / 1991 / Finite type integral submanifolds of the contact manifold R2n+1(-3) / Bull. Inst. Math. Acad. Sinica 19 (4) : 327 ~ 350
C. Baikoussis / 1994 / On Legendre curves in contact 3-manifolds / Geom. Dedicata 49 (2) : 135 ~ 142
C. Camci / / On a curve with torsion is equal to 1 in 3-dimensional Sasakian manifold, Preprint
C. Camci / 2007 / A curves theory in contact geometry / 박사 / Ankara University
C. Baikoussis / 1991 / Finite type integral submanifolds of the contact manifold R2n+1(-3) / Bull. Inst. Math. Acad. Sinica 19 (4) : 327 ~ 350
C. Baikoussis / 1994 / On Legendre curves in contact 3-manifolds / Geom. Dedicata 49 (2) : 135 ~ 142
C. Camci / / On a curve with torsion is equal to 1 in 3-dimensional Sasakian manifold, Preprint
C. Camci / 2007 / A curves theory in contact geometry / 박사 / Ankara University
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