Some special curves in three dimensional f-Kenmotsu manifolds
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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').
Abstract
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').
참고문헌 (23)
- J. Arroya, "When is a periodic function the curvature of a closed plane curve?", The American Mathematical Monthly, 115, pp.405~414 (2008)
- C. Baikoussis, "On Legendre curves in contact 3-manifolds", Geom. Dedi-cata, 49, pp.135~142 (1994)
- M. Belkhalfa, "On Legendre curves in Rie-mannian and Sasakian spaces", Soochow J. Math, 28, pp.81~91 (2002)
- D.E. Blair, "Contact manifolds in Riemannian geometry" (1976), Springer-Verlag
- D.E. Blair, "Riemannian Geometry of contact and symplectic manifolds" (2010), Birkhauser
- B. Y. Chen, "Biharmonic surfaces in pseudo Euclidean spaces", Mem. Fac. Sci. Kyushu Univ. Ser. A, 45, pp.323~347 (1991)
- J.L. Cabrerizo, "The contact magnetic ow in 3D Sasakian manifolds", J. Phys. A.Math., Theor., 42, pp.195201~ (2009)
- R. Caddeo, "Biharmonic curves on a surface", Rend, Mat. Appl, 21, pp.143~157 (2001)
- J.T. Cho, "On slant curves in Sasakian 3-manifolds", Bull. Austral. Math. Soc., 74, pp.359~367 (2006)
- C. Calin, "From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds", Bull. Malays. Math. Soc., 33, pp.361~368 (2010)
- P.Do Carmo, "Riemannian Geometry" (1992), Birkhauser Boston
- Dorel Fetcu, "Biharmonic Legendre curves in Sasakian space forms", 대한수학회지, 45(2), pp.393~404 (2008), 대한수학회
- Jun-ichi Inoguchi, "BIMINIMAL CURVES IN 2-DIMENSIONAL SPACE FORMS", 대한수학회논문집, 27(4), pp.771~780 (2012), 대한수학회
- J.I. Inoguchi, "Submanifolds with harmonic mean curvature vector field in contact 3-manifold", Cooloq. Math., 100, pp.163~167 (2004)
- H. Kocayigit, "1-Type curves and biharmonic curves in euclidean 3-space", Int. Elec. J. Geo., 4, pp.97~101 (2011)
- K. Kenmotsu, "A class of almost contact Riemannian manifolds", Tohoku Math. J., 24, pp.93~103 (1972)
- S. Montaldo, "A short survey on biharmonic maps between Riemannian manifolds", Rev. Un. Mat. Argentina, 47, pp.1~22 (2006)
- Pradip Majhi, "Almost Ricci Soliton and Gradient Almost Ricci Soliton on $3$-dimensional $f$-Kenmotsu Manifolds", Kyungpook Mathematical Journal, 57(2), pp.309~318 (2017), 경북대학교 자연과학대학 수학과
- Z. Olszak, "Normal locally conformal almost cosymplectic manifolds", Publ. Math. Debrecen, 39, pp.315~323 (1991)
- Z. Olszak, "Locally conformal almost cosymplectic manifolds", Colloq. Math., 57, pp.73~87 (1989)
- G. Pitis, "A remark on Kenmotsu manifolds", Bul. Univ. Brasov Ser. C, 30, pp.31~32 (1988)
- A. Sarkar, "Legendre curves on three dimensional Heisenberg Groups", Facta Universitatis, 28, pp.241~248 (2013)
- J. Welyczko, "On Legendre curves in 3-dimensional normal almost contact metric man-ifolds", Soochow J. Math., 33, pp.929~937 (2007)