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In this paper we study Biharmonic curves, Legendre curves and Magnetic curves in three dimensional $f$-Kenmotsu manifolds. We also study $1$-type curves in a three dimensional $f$-Kenmotsu manifold by using the mean curvature vector field of the curve. As a consequence we obtain for a biharmonic helix in a three dimensional $f$-Kenmotsu manifold with the curvature $\kappa$ and the torsion $\tau$, $\kappa^{2} + \tau^{2} = -(f^{2} +f^{\prime})$. Also we prove that if a $1$-type non-geodesic biharmonic curve $\gamma$ is helix, then $\lambda = -(f^{2} + f').
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참고문헌 (23)
참고문헌 신청
J. Arroya / 2008 / When is a periodic function the curvature of a closed plane curve? / The American Mathematical Monthly 115:405~414
C. Baikoussis / 1994 / On Legendre curves in contact 3-manifolds / Geom. Dedi-cata 49:135~142
M. Belkhalfa / 2002 / On Legendre curves in Rie-mannian and Sasakian spaces / Soochow J. Math 28:81~91
D.E. Blair / 1976 / Contact manifolds in Riemannian geometry / Springer-Verlag
D.E. Blair / 2010 / Riemannian Geometry of contact and symplectic manifolds / Birkhauser
C. Baikoussis / 1994 / On Legendre curves in contact 3-manifolds / Geom. Dedi-cata 49:135~142
M. Belkhalfa / 2002 / On Legendre curves in Rie-mannian and Sasakian spaces / Soochow J. Math 28:81~91
D.E. Blair / 1976 / Contact manifolds in Riemannian geometry / Springer-Verlag
D.E. Blair / 2010 / Riemannian Geometry of contact and symplectic manifolds / Birkhauser
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