The investigation of some special curves in the pseudo-Galilean 4-space $G_{1}^{4} $
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912613251678208 |
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| author | Almaz, Fatma Oztekin, Handan |
| author_facet | Almaz, Fatma Oztekin, Handan |
| contents | In this paper, we investigate and characterise an arbitrary admissible curve in terms of its curvature functions in the pseudo-Galilean space $G_{1}^{4}$% . We also give some special curves in four-dimensional pseudo-Galilean space and their characterisations, such as position curve, osculating curve, normal curve, rectifying curve, slant helices, and spherical curves. Moreover, this study provides classifications of admissible curves in $G_{1}^{4}$. That is, the admissible rectifying curves lying fully in the $G_{1}^{4}$ are expressed and given necessary and sufficient conditions for such a curve to be an admissible rectifying curve, osculating curve, normal curve, slant helices and spherical curves in $G_{1}^{4}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The investigation of some special curves in the pseudo-Galilean 4-space $G_{1}^{4} $ Almaz, Fatma Oztekin, Handan Differential Geometry Algebraic Geometry 53A35, 53B30, 53C40 In this paper, we investigate and characterise an arbitrary admissible curve in terms of its curvature functions in the pseudo-Galilean space $G_{1}^{4}$% . We also give some special curves in four-dimensional pseudo-Galilean space and their characterisations, such as position curve, osculating curve, normal curve, rectifying curve, slant helices, and spherical curves. Moreover, this study provides classifications of admissible curves in $G_{1}^{4}$. That is, the admissible rectifying curves lying fully in the $G_{1}^{4}$ are expressed and given necessary and sufficient conditions for such a curve to be an admissible rectifying curve, osculating curve, normal curve, slant helices and spherical curves in $G_{1}^{4}$. |
| title | The investigation of some special curves in the pseudo-Galilean 4-space $G_{1}^{4} $ |
| topic | Differential Geometry Algebraic Geometry 53A35, 53B30, 53C40 |
| url | https://arxiv.org/abs/2509.24061 |