Framed null curves and timelike surfaces via Lorentzian harmonic maps into de-Sitter 2-space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908837511954432 |
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| author | Akamine, Shintaro Kiyohara, Hirotaka |
| author_facet | Akamine, Shintaro Kiyohara, Hirotaka |
| contents | We construct a class of Lorentzian harmonic maps into the de-Sitter $2$-space satisfying the eigenvalue equation $\Box N=2H^2N$ for the d'Alambert operator $\Box$ and a non-zero constant $H$ from framed null curves. We also investigate two classes of timelike surfaces associated with these Lorentzian harmonic maps: the first one is timelike surfaces with constant mean curvature $H$ in Lorentz-Minkowski $3$-space and the second one is timelike minimal surfaces in the three-dimensional Lorentzian Heisenberg group $\operatorname{Nil}_3(H)$. In particular, we characterize some properties of singularities on timelike minimal surfaces in $\operatorname{Nil}_3(H)$ via an invariant of framed null curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Framed null curves and timelike surfaces via Lorentzian harmonic maps into de-Sitter 2-space Akamine, Shintaro Kiyohara, Hirotaka Differential Geometry Primary 53A10, Secondary 53B30, 57R45 We construct a class of Lorentzian harmonic maps into the de-Sitter $2$-space satisfying the eigenvalue equation $\Box N=2H^2N$ for the d'Alambert operator $\Box$ and a non-zero constant $H$ from framed null curves. We also investigate two classes of timelike surfaces associated with these Lorentzian harmonic maps: the first one is timelike surfaces with constant mean curvature $H$ in Lorentz-Minkowski $3$-space and the second one is timelike minimal surfaces in the three-dimensional Lorentzian Heisenberg group $\operatorname{Nil}_3(H)$. In particular, we characterize some properties of singularities on timelike minimal surfaces in $\operatorname{Nil}_3(H)$ via an invariant of framed null curves. |
| title | Framed null curves and timelike surfaces via Lorentzian harmonic maps into de-Sitter 2-space |
| topic | Differential Geometry Primary 53A10, Secondary 53B30, 57R45 |
| url | https://arxiv.org/abs/2602.15415 |