A New Kind of Slant Helix in Lorentzian (n + 2)−Spaces
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In this paper, we introduce a new kindof slant helix for null curves called null $W_{n}-$slant helix and we give adefinition of new harmonic curvature functions of a null curve in terms of $%W_{n}$ in $(n+2)-$dimensional Lorentzian space $M_{1}^{n+2}$ (for $n>3$). Also, we obtain a characterization such as:\begin{equation*}\text{\textquotedblleft The curve }\alpha \ \text{is a null }W_{n}-\text{%slant helix }\Leftrightarrow H_{n}^{^{\prime }}-k_{1}H_{n-1}-k_{2}H_{n-3}=0"\end{equation*}%where $H_{n},H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $%k_{1},k_{2}$ are the Cartan curvature functions of the null curve $\alpha $.
Abstract
In this paper, we introduce a new kindof slant helix for null curves called null $W_{n}-$slant helix and we give adefinition of new harmonic curvature functions of a null curve in terms of $%W_{n}$ in $(n+2)-$dimensional Lorentzian space $M_{1}^{n+2}$ (for $n>3$). Also, we obtain a characterization such as:\begin{equation*}\text{\textquotedblleft The curve }\alpha \ \text{is a null }W_{n}-\text{%slant helix }\Leftrightarrow H_{n}^{^{\prime }}-k_{1}H_{n-1}-k_{2}H_{n-3}=0"\end{equation*}%where $H_{n},H_{n-1}$ and $H_{n-3}$ are harmonic curvature functions and $%k_{1},k_{2}$ are the Cartan curvature functions of the null curve $\alpha $.
참고문헌 (17)
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