Biharmonic curves in 3-dimensional Sasakian space forms |
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| Authors: | Jong Taek Cho Jun-Ichi Inoguchi Ji-Eun Lee |
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| Affiliation: | (1) Department of Mathematics, Chonnam National University, CNU The Institute of Basic Science, Kwangju, 500–757, South Korea;(2) Department of Mathematics Education, Faculty of Education, Utsunomiya University, Minemachi 350, Utsunomiya 321–8505, Japan;(3) Department of Mathematics, Graduate School, Chonnam National University, Kwangju, 500–757, South Korea |
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| Abstract: | We show that every proper biharmonic curve in a 3-dimensional Sasakian space form of constant holomorphic sectional curvature H is a helix (both of whose geodesic curvature and geodesic torsion are constants). In particular, if H ≠ 1, then it is a slant helix, that is, a helix which makes constant angle α with the Reeb vector field with the property  . Moreover, we construct parametric equations of proper biharmonic herices in Bianchi–Cartan–Vranceanu model spaces of a Sasakian space form. |
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| Keywords: | Harmonic and biharmonic curves Sasakian space forms Bianchi– Cartan– Vranceanu model spaces |
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