Spinor representation in isotropic 3-space via Laguerre geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866913700885037056 |
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| author | Cho, Joseph Lee, Dami Lee, Wonjoo Yang, Seong-Deog |
| author_facet | Cho, Joseph Lee, Dami Lee, Wonjoo Yang, Seong-Deog |
| contents | We give a detailed description of the geometry of isotropic space, in parallel to those of Euclidean space within the realm of Laguerre geometry. After developing basic surface theory in isotropic space, we define spin transformations, directly leading to the spinor representation of conformal surfaces in isotropic space. As an application, we obtain the Weierstrass-type representation for zero mean curvature surfaces, and the Kenmotsu-type representation for constant mean curvature surfaces, allowing us to construct many explicit examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13677 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spinor representation in isotropic 3-space via Laguerre geometry Cho, Joseph Lee, Dami Lee, Wonjoo Yang, Seong-Deog Differential Geometry (2020): 53A10 (Primary) 53B30 (Secondary) We give a detailed description of the geometry of isotropic space, in parallel to those of Euclidean space within the realm of Laguerre geometry. After developing basic surface theory in isotropic space, we define spin transformations, directly leading to the spinor representation of conformal surfaces in isotropic space. As an application, we obtain the Weierstrass-type representation for zero mean curvature surfaces, and the Kenmotsu-type representation for constant mean curvature surfaces, allowing us to construct many explicit examples. |
| title | Spinor representation in isotropic 3-space via Laguerre geometry |
| topic | Differential Geometry (2020): 53A10 (Primary) 53B30 (Secondary) |
| url | https://arxiv.org/abs/2303.13677 |