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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2410.22955 |
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| _version_ | 1866929568593477632 |
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| author | Csima, Géza Szirmai, Jenő |
| author_facet | Csima, Géza Szirmai, Jenő |
| contents | In the present paper we deal with non-constant curvature Thurston geometries \cite{M97}, \cite{S}, \cite{Sz22-3},\cite{W06}. We define and determine the generalized trans\-lation-like Apollonius surfaces and thus also bisector surfaces as a special case. Moreover, we give a possible definition of the "surface of a translation-like triangle" in each investigated geometry. In our work we will use the projective model of Thurston geometries described by E. Molnár in \cite{M97}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Translation-like Apollonius and triangular surfaces in non-constant curvature Thurston geometries Csima, Géza Szirmai, Jenő Metric Geometry 53A20, 53A35, 52C35, 53B20 In the present paper we deal with non-constant curvature Thurston geometries \cite{M97}, \cite{S}, \cite{Sz22-3},\cite{W06}. We define and determine the generalized trans\-lation-like Apollonius surfaces and thus also bisector surfaces as a special case. Moreover, we give a possible definition of the "surface of a translation-like triangle" in each investigated geometry. In our work we will use the projective model of Thurston geometries described by E. Molnár in \cite{M97}. |
| title | Translation-like Apollonius and triangular surfaces in non-constant curvature Thurston geometries |
| topic | Metric Geometry 53A20, 53A35, 52C35, 53B20 |
| url | https://arxiv.org/abs/2410.22955 |