Harmonic 1-Type Curves and Weak Biharmonic Curves in Lorentzian 3-Space

Abstract

We study 1-type curves by using the mean curvature vector field of the curve. We also study biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for them in the Euclidean 3-space. Moreover we give some characterizations and results for a Frenet curve in the same space.

Slant Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds

“…The Cartan frame is a frame with the minimum number of curvature functions which are invariant under Lorentzian transformation (see [11][12][13]19]).…”

On C-parallel legendre curves in non-Sasakian contact metric manifolds

“…In [2], Kılıç and Arslan studied Euclidean submanifolds satisfying ∆ ⊥ H = λH. In [12], Kocayigit and Hacısalihoglu studied curves satisying ∆H = λH in a 3-dimensional Riemannian manifold. For Legendre curves in Sasakian manifolds, same problems were studied by Inoguchi in [10].…”

Harmonicity and differential equation of involute of a curve in E3

“…Thanks to meticulous studies, it has been revealed that curves can be classified [6]. After this classification, a great many number of articles have been written, [7,8] and also [9]. In this paper, we first take a unit speed curve which we call through the work as main curve, then write the characterizations of an involute curve by means of Frenet apparatus of the main curve.…”

“…is called a Laplace operator [7,8]. Let α be the unit speed curve and H be the mean curvature vector field along the curve α.…”