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- Title
Slant curves and biharmonic Frenet curves in 3-dimensional para-Sasakian manifolds.
- Authors
Ji-Eun Lee
- Abstract
In this paper, we study slant Frenet curves, slant curves with null normal and null slant curves in a 3-dimensional para-Sasakian manifold. A non-geodesic curve γ in a para-Sasakian 3-manifold M³ is a slant curve if and only if η(N) = 0. Next, we find that for a slant Frenet curve in a 3-dimensional para-Sasakian manifold, the ratio of κ and τ + 1 is constant (cf.[11]). There does not exist non-geodesic slant curves with null normals in a 3-dimensional para-Sasakian manifold for η(γ')² = a² ≠ 1. Moreover, we construct para-Bianchi-Cartan-Vr˘anceanu model with 3-dimensional para-Sasakian structure and find the necessary and sufficient conditions for proper biharmonic Frenet curve. In particular, we prove that the biharmonic Frenet curves in Hyperbolic Heisenberg group are slant curves and find the parametric equations of them.
- Subjects
BIHARMONIC equations; HYPERBOLIC groups; PARAMETRIC equations
- Publication
Balkan Journal of Geometry & Its Applications, 2021, Vol 26, Issue 1, p21
- ISSN
1224-2780
- Publication type
Article