Abstract
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 .
Highlights
The notion of slant curves was introduced in [1] for a contact Riemannian three-manifold, that is, a curve in a contact three-manifold is said to be slant if its tangent vector field has a constant angle with the Reeb vector field
In [2], we showed that proper biharmonic curves are helices in three-dimensional e (= 2c − 3)
We study the slant curves in Lorentzian Sasakian space forms of constant
Summary
The notion of slant curves was introduced in [1] for a contact Riemannian three-manifold, that is, a curve in a contact three-manifold is said to be slant if its tangent vector field has a constant angle with the Reeb vector field. If H e 6= 1, Sasakian space forms of constant holomorphic sectional curvature H it is a slant helix; that is, a helix such that η (γ0 ) = cos α0 is a constant, with κ 2 + τ 2 = 1 +. That proper biharmonic Frenet curves are pseudo-helices in three-dimensional Lorentzian Sasakian space forms of constant holomorphic sectional curvature H (= 2c + 3). We study the slant curves in Lorentzian Sasakian space forms of constant. Perrone [5,6] showed that the notion of non-degenerate almost CR structures is equivalent to the notion of contact pseudo-metric structures He defined the generalized Tanaka–Websterin a contact pseudo-metric manifold.
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