In this paper, we study slant helix using modified orthogonal frame in Minkowski space E31 with timelike, lightlike and spacelike axes. We also a general the Killing vector field axis. Furthermore, give non-trivial example find relations for curvature torsion of f-biharmonic helix.

Abstract This paper is devoted to examine necessary and sufficient conditions for a Frenet curve be f -harmonic, -biharmonic, bi- -harmonic -biminimal in three-dimensional $$\beta $$ β -Kenmotsu manifolds. In addition, such are investigated slant curves.

This is a supplement to our previous research note [3]. In [3], we gave a characterization of biharmonic curves in Minkowski 3-space. More precisely, we pointed out that every biharmonic curves with nonnull principal normal in Minkowski 3-space is a helix, whose curvature κ and torsion τ satisfy κ2 = τ2. In the classification of biharmonic curves in Minkowski 3-space due to Chen and Ishikawa [1...

Motion of a biharmonic system under action of small periodic force and small damped force is studied. The biharmonic oscillator is a physical system acting under a biharmonic force like: θ θ 2 sin sin b a + . The article contains biharmonic oscillator analysis, phase space research, and analytic solutions for separatrixes. The biharmonic oscillator performs chaotic motion near separatrixes unde...

For a domain R and a Riemannian manifold N R. If u 2 W ( ; N) is an extrinsic (or intrinsic, respectively) biharmonic map. Then u 2 C( ; N). x

We prove that a stationary extrinsic (or intrinsic, respectively) biharmonic map u 2 W ( ; N) from R into a Riemnanian manifold N is smooth away from a closed set of (m 4)-dimensional Hausdor measure zero. x

In this paper, non-geodesic biharmonic curves in ̃ SL(2, R) space are characterized and the statement that only proper biharmonic curves are helices is proved. Also, the explicit parametric equations of proper biharmonic helices are obtained. AMS subject classifications: 53A40