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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2603.28779 |
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| _version_ | 1866912989733453824 |
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| author | Almaz, Fatma Diken, Hazel |
| author_facet | Almaz, Fatma Diken, Hazel |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28779 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A generalisation of g-rectifying and g-normal curves in Lorentzian n-space Almaz, Fatma Diken, Hazel Differential Geometry 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. |
| title | A generalisation of g-rectifying and g-normal curves in Lorentzian n-space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.28779 |