Relation between the minimal Lorentz surfaces in $\mathbb R^4_2$ and $\mathbb R^3_1$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914693491195904 |
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| author | Kanchev, Krasimir Kassabov, Ognian Milousheva, Velichka |
| author_facet | Kanchev, Krasimir Kassabov, Ognian Milousheva, Velichka |
| contents | In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space $\mathbb R^3_1$ using real-valued functions. Applying the Weierstrass-type representations for the null curves, we find a correspondence between the null curves in $\mathbb R^4_2$ and the pairs of null curves in $\mathbb R^3_1$. Based on this correspondence, we obtain a relation between the minimal Lorentz surfaces in $\mathbb R^4_2$ and the pairs of minimal Lorentz surfaces in $\mathbb R^3_1$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relation between the minimal Lorentz surfaces in $\mathbb R^4_2$ and $\mathbb R^3_1$ Kanchev, Krasimir Kassabov, Ognian Milousheva, Velichka Differential Geometry 53B30 (Primary), 53A35, 53A10, 53B25 (Secondary) In this paper we give Weierstrass-type representation formulas for the null curves and for the minimal Lorentz surfaces in the Minkowski 3-space $\mathbb R^3_1$ using real-valued functions. Applying the Weierstrass-type representations for the null curves, we find a correspondence between the null curves in $\mathbb R^4_2$ and the pairs of null curves in $\mathbb R^3_1$. Based on this correspondence, we obtain a relation between the minimal Lorentz surfaces in $\mathbb R^4_2$ and the pairs of minimal Lorentz surfaces in $\mathbb R^3_1$. |
| title | Relation between the minimal Lorentz surfaces in $\mathbb R^4_2$ and $\mathbb R^3_1$ |
| topic | Differential Geometry 53B30 (Primary), 53A35, 53A10, 53B25 (Secondary) |
| url | https://arxiv.org/abs/2402.17850 |