Slant Curves in Contact Lorentzian Manifolds with CR Structures

Ji-Eun Lee
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Ji-Eun Lee: Institute of Basic Science, Chonnam National University, Gwangju 61186, Korea

Mathematics, 2020, vol. 8, issue 1, 1-11

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 .

Keywords: slant curves; Jacobi equation; CR structure; Lorentzian Sasakian space forms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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