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Journals / International Electronic Journal of Geometry / 2020 / Cilt: 13 - Sayı: 2

On Slant Curves in Sasakian Lorentzian 3-Manifolds

Ji - Eun LEE
Pages
108–115
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

For example, we find slant pseudo-helix in Lorentzian Heisenberg 3-space.

📌 3 Key Takeaways

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Objective & Hypothesis: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.
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Key Findings & Data: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 $\kappa^2=\tau^2$.
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Conclusion & Impact:For example, we find slant pseudo-helix in Lorentzian Heisenberg 3-space.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Slant Curves · Legendre curve · Sasakian Lorentzian manifold

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.

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Cite This Article

LEE, J. -. E. (2022). On Slant Curves in Sasakian Lorentzian 3-Manifolds. International Electronic Journal of Geometry, Cilt: 13 - Sayı: 2, 108–115. https://ajindex.com/articles/539609

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