DOI QR코드

DOI QR Code

FINITE TYPE CURVE IN 3-DIMENSIONAL SASAKIAN MANIFOLD

  • Camci, Cetin ;
  • Hacisalihoglu, H. Hilmi
  • 투고 : 2009.03.11
  • 발행 : 2010.11.30

초록

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.

키워드

Sasakian Manifold;Legendre curve;finite type curve

참고문헌

  1. C. Baikoussis and D. E. Blair, Finite type integral submanifolds of the contact manifold $R^{2n+1}(-3)$, Bull. Inst. Math. Acad. Sinica 19 (1991), no. 4, 327-350.
  2. C. Baikoussis and D. E. Blair, On Legendre curves in contact 3-manifolds, Geom. Dedicata 49 (1994), no. 2, 135-142. https://doi.org/10.1007/BF01610616
  3. D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics, Vol. 509. Springer-Verlag, Berlin-New York, 1976.
  4. C. Camci, A curves theory in contact geometry, Ph. D. Thesis, Ankara University, 2007.
  5. C. Camci and C. Ozgur, On a curve with torsion is equal to 1 in 3-dimensional Sasakian manifold, Preprint.
  6. B. Y. Chen, J. Dillen, F. Verstraelen, and L. Vrancken, Curves of finite type, Geometry and topology of submanifolds, II (Avignon, 1988), 76-110, World Sci. Publ., Teaneck, NJ, 1990.
  7. J. T. Cho, J.-I. Inoguchi, and J.-E. Lee, On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc. 74 (2006), no. 3, 359-367. https://doi.org/10.1017/S0004972700040429
  8. T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966), 380-385. https://doi.org/10.2969/jmsj/01840380

피인용 문헌

  1. On ruled surface in 3-dimensional almost contact metric manifold vol.14, pp.05, 2017, https://doi.org/10.1142/S0219887817500761