LEGENDRE CURVES ON 3-DIMENSIONAL f-KENMOTSU MANIFOLDS ADMITTING SCHOUTEN-VAN KAMPEN CONNECTION

In the present paper, biharmonic Legendre curves with respect to Schouten-Van Kampen connection have been studied on three-dimensional f-Kenmotsu manifolds. Locally $\phi $-symmetric Legendre curves on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen Connection have been introduced.Also slant curves have been studied on three-dimensional f-Kenmotsu manifolds with respect to Schouten-Van Kampen connection. Finally, we constract an example of a Legendre curve in a 3-dimensional f-Kenmotsu manifold.

Slant Curves in Contact Lorentzian Manifolds with CR Structures

In this paper, we first find the properties of the generalized Tanaka–Webster connection in a contact Lorentzian manifold. Next, we find that a necessary and sufficient condition for the ∇ ^ -geodesic is a magnetic curve (for ∇) along slant curves. Finally, we prove that when c ≤ 0 , there does not exist a non-geodesic slant Frenet curve satisfying the ∇ ^ -Jacobi equations for the ∇ ^ -geodesic vector fields in M. Thus, we construct the explicit parametric equations of pseudo-Hermitian pseudo-helices in Lorentzian space forms M 1 3 ( H ^ ) for H ^ = 2 c > 0 .

Slant Curve in Lorentzian BCV Spaces

The aim of this study is to examine the slant curves in Lorentzian manifolds with BCV (Bianchi-Cartan-Vranceanu) metrics. A practical form of the directional derivative in the presence of the BCV metrics is presented. Moreover, some theorems for slant curves in Lorentzian BCV manifolds are proved.

Slant Curves and Contact Magnetic Curves in Sasakian Lorentzian 3-Manifolds

In this article, we define Lorentzian cross product in a three-dimensional almost contact Lorentzian manifold. Using a Lorentzian cross product, we prove that the ratio of κ and τ − 1 is constant along a Frenet slant curve in a Sasakian Lorentzian three-manifold. Moreover, we prove that γ is a slant curve if and only if M is Sasakian for a contact magnetic curve γ in contact Lorentzian three-manifold M. As an example, we find contact magnetic curves in Lorentzian Heisenberg three-space.

C-parallel and C-proper slant curves of S-manifolds

In the present paper, we define and study C-parallel and C-proper slant curves of S-manifolds. We prove that a slant curve in an S-manifold of order r ? 3, under certain conditions, is C-parallel or C-parallel in the normal bundle if and only if it is a non-Legendre slant helix or Legendre helix, respectively. Moreover, under certain conditions, we show that is C-proper or C-proper in the normal bundle if and only if it is a non-Legendre slant curve or Legendre curve, respectively. We also give two examples of such curves in R2m+s(-3s).

Legendre curves on 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection

The object of the present paper is to study biharmonic Legendre curves, locally ?-symmetric Legendre curves and slant curves in 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection. Finally, we construct an example of a Legendre curve in a 3-dimensional Kenmotsu manifold.