On Slant Curves in Sasakian Lorentzian 3-Manifolds

Year 2020, , 108 - 115, 15.10.2020

Ji-eun Lee

https://doi.org/10.36890/iejg.595442

Abstract

In this paper,  we study $C$-parallel mean curvature vector field and $C$-proper mean curvature vector field along a slant Frenet curve in a Sasakian Lorentzian 3-manifold. In particular, we prove that a slant Frenet curve $\gamma$ in a Sasakian Lorentzian $3$-manifold $M$ satisfying $\Delta_{\dot{\gamma}} H =0$ is a geodesic or pseudo-helix with $\kappa^2=\tau^2$. For example, we find slant pseudo-helix in Lorentzian Heisenberg 3-space.                                                                                                                                                                                

Keywords

Slant Curves, Legendre curve, Sasakian Lorentzian manifold

Supporting Institution

National Research Foundation of Korea (NRF)

Project Number

NRF-2019R1l1A1A01043457

Thanks

The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1l1A1A01043457).

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