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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28779 |
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Table of Contents:
- In this paper, we introduce and analyze $g-$rectifying curves (spacelike and null curves) and $\ g-$normal curves in Lorentzian $n$-space, building upon the established notion of rectifying curves and normal curve, respectively. Our generalization extends this definition by considering an $% g-$position vector field, $ξ_{g}(s)=\int g(s)dξ$, where $g$ is an integrable function in the arc-length parameter $s$. An $g$-rectifying curves(or $g-$normal curves) are then defined as an arc-length parametrized curve $ξ$ in Lorentzian $n-$space such that its $g$-position vector consistently lies within its rectifying space(or normal space). The primary objective of this work is to provide a comprehensive characterization and classification of these $g$-rectifying curves and $g-$normal curves, thereby expanding the geometric understanding of curves in Lorentzian $n$-spaces.