Some Curves on Three Dimensional Kenmotsu Space Forms

The object of the present paper is to study slant curves, $C$-parallel slant curves on Kenmotsu space forms. As a particular case we consider Legendre curves and integral curves of the Reeb vector fields. We show that on such manifolds Legendre curves do not exist and the slant integral curves of the Reeb vector fields are a geodesics. We also study biharmonic curves on such manifolds. An example is given.

Keywords:

Kenmotsu space forms, Legendre curves slant curves,

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[1] Baikoussis, C., and Blair, D. E., On Legendre curves in contact 3-manifolds, Geom. Dedicata, 49 (1994), 135-142.
[2] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Progress in Math., Vol 203 Barkhauser, Boston (2002).
[3] Sarkar, A., Mondal, Ashis., Certain curves on some classes of three-dimensional manifolds, Revista de la unoin Mathematica Argentina, 58(2017), 107-125.
[4] Cho, J. T. and Lee, J. E., Slant curves in contact Pseudo-Hermition manifolds, Bull. Austral. Math. Soc.78 (2008), 383-396.
[5] Gu¨venc, S. and Özgur, C., On slant curves in trans-Sasakian manifolds, Revista De La Union Mat Argentina, 55(2014), 81-100.
[6] Özgur, C., and Gu¨venc, S., On some classes of biharmonic Legendre curves in generalized Sasakian space forms, Collect. Math., 65(2014), 203-218.
[7] Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1972), 93-103.

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2013
Yayıncı: Mehmet Zeki SARIKAYA

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