In this article, we mainly discuss the local differential geometrical properties of the lightlike Killing magnetic curve $ \mathit{\boldsymbol{\gamma }}(s) $ in $ \mathbb{S}^{3}_{1} $ with a magnetic field $ \boldsymbol{ V} $. Here, a new Frenet frame $ \{\mathit{\boldsymbol{\gamma }}, \boldsymbol{ T}, \boldsymbol{ N}, \boldsymbol{ B}\} $ is established, and we obtain the local structure of $ \mathit{\boldsymbol{\gamma }}(s) $. Moreover, the singular properties of the binormal lightlike surface of the $ \mathit{\boldsymbol{\gamma }}(s) $ are given. Finally, an example is used to understand the main results of the paper.
Citation: Xiaoyan Jiang, Jianguo Sun. Local geometric properties of the lightlike Killing magnetic curves in de Sitter 3-space[J]. AIMS Mathematics, 2021, 6(11): 12543-12559. doi: 10.3934/math.2021723
In this article, we mainly discuss the local differential geometrical properties of the lightlike Killing magnetic curve $ \mathit{\boldsymbol{\gamma }}(s) $ in $ \mathbb{S}^{3}_{1} $ with a magnetic field $ \boldsymbol{ V} $. Here, a new Frenet frame $ \{\mathit{\boldsymbol{\gamma }}, \boldsymbol{ T}, \boldsymbol{ N}, \boldsymbol{ B}\} $ is established, and we obtain the local structure of $ \mathit{\boldsymbol{\gamma }}(s) $. Moreover, the singular properties of the binormal lightlike surface of the $ \mathit{\boldsymbol{\gamma }}(s) $ are given. Finally, an example is used to understand the main results of the paper.
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Xiaoyan Jiang, Jianguo Sun. Local geometric properties of the lightlike Killing magnetic curves in de Sitter 3-space[J]. AIMS Mathematics, 2021, 6(11): 12543-12559. doi: 10.3934/math.2021723
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