• 대한수학회지
• /
• 제51권6호
• /
• pp.1105-1122
• /
• 2014

Biharmonic curves are a generalization of geodesics, with applications in elasticity theory and computer science. The paper proposes a first study of biharmonic curves in spaces with Finslerian geometry, covering the following topics: a deduction of their equations, specific properties and existence of non-geodesic biharmonic curves for some classes of Finsler spaces. Integration of the biharmonic equation is presented for two concrete Finsler metrics.

• 대한수학회지
• /
• 제45권2호
• /
• pp.393-404
• /
• 2008

Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.

• 호남수학학술지
• /
• 제39권4호
• /
• pp.515-525
• /
• 2017

In this paper, we study planar normal section curves. We have interpreted curvatures of normal section curves. On the other hand we have investigated sufficient and necessary conditions for a normal section curve to be biharmonic.

• 대한수학회논문집
• /
• 제35권3호
• /
• pp.967-977
• /
• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제27권2호
• /
• pp.83-96
• /
• 2020

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 κ and the torsion τ, κ² + τ² = -(f² + f'). Also we prove that if a 1-type non-geodesic biharmonic curve γ is helix, then λ = -(f² + f').

• 대한수학회논문집
• /
• 제33권4호
• /
• pp.1309-1320
• /
• 2018

In this paper, we show that proper biharmonic spacelike curve ${\gamma}$ in Lorentzian Heisenberg space (${\mathbb{H}}_3$, g) is pseudo-helix with ${\kappa}^2-{\tau}^2=-1+4{\eta}(B)^2$. Moreover, ${\gamma}$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

• 대한수학회보
• /
• 제53권3호
• /
• pp.723-732
• /
• 2016

We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifold. Moreover, we determine 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds which admit a certain kind of proper biharmonic foliation.

• 대한수학회논문집
• /
• 제33권1호
• /
• pp.293-303
• /
• 2018

In this paper, we consider biharmonic slant curves in S-space forms. We obtain a main theorem, which gives us four different cases to find curvature conditions for these curves. We also give examples of slant curves in ${\mathbb{R}}^{2n+s}(-3s)$.

• Kyungpook Mathematical Journal
• /
• 제59권1호
• /
• pp.135-147
• /
• 2019

In this paper we study some properties of Riemannian manifolds, we construct a new example of non-harmonic biharmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.

• Kyungpook Mathematical Journal
• /
• 제55권1호
• /
• pp.157-168
• /
• 2015

In this paper, we prove that every f-biharmonic map from a complete Riemannian manifold into a Riemannian manifold with non-positive sectional curvature,satisfying some condition, is f-harmonic. Also we present some properties for the f-biharmonicity of submanifolds of $\mathbb{S}^n$, and we give the classification of f-biharmonic curves in 3-dimensional sphere.