Discrete Weierstrass-type representations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929441881456640 |
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| author | Pember, Mason Polly, Denis Yasumoto, Masashi |
| author_facet | Pember, Mason Polly, Denis Yasumoto, Masashi |
| contents | Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes can be viewed as applications of the $Ω$-dual transform to lightlike Gauss maps in Laguerre geometry. From this construction, further Weierstrass-type representations arise. As an application of the techniques we develop, we show that all discrete linear Weingarten surfaces of Bryant or Bianchi type locally arise via Weierstrass-type representations from discrete holomorhpic maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_06774 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Discrete Weierstrass-type representations Pember, Mason Polly, Denis Yasumoto, Masashi Differential Geometry 53A70 (primary), 51B15 (secondary) Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes can be viewed as applications of the $Ω$-dual transform to lightlike Gauss maps in Laguerre geometry. From this construction, further Weierstrass-type representations arise. As an application of the techniques we develop, we show that all discrete linear Weingarten surfaces of Bryant or Bianchi type locally arise via Weierstrass-type representations from discrete holomorhpic maps. |
| title | Discrete Weierstrass-type representations |
| topic | Differential Geometry 53A70 (primary), 51B15 (secondary) |
| url | https://arxiv.org/abs/2105.06774 |