Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917661724639232 |
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| author | Csima, Géza Szirmai, Jenő |
| author_facet | Csima, Géza Szirmai, Jenő |
| contents | After having investigated the geodesic triangles and their angle sums in Nil and $Sl\times\mathbb{R}$ geometries we consider the analogous problem in Sol space that is one of the eight 3-dimensional Thurston geometries. We analyse the interior angle sums of geodesic triangles and we prove that it can be larger than, less than or equal to $π$. Moreover, we determine the equations of Sol isoptic surfaces of translation-like segments and as a special case of this we examine the Sol translation-like Thales sphere, which we call Thaloid. We also discuss the behavior of this surface. In our work we will use the projective model of Sol described by E. Molnár in \cite{M97}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry Csima, Géza Szirmai, Jenő Metric Geometry 53A20, 53A35, 52C35, 53B20 After having investigated the geodesic triangles and their angle sums in Nil and $Sl\times\mathbb{R}$ geometries we consider the analogous problem in Sol space that is one of the eight 3-dimensional Thurston geometries. We analyse the interior angle sums of geodesic triangles and we prove that it can be larger than, less than or equal to $π$. Moreover, we determine the equations of Sol isoptic surfaces of translation-like segments and as a special case of this we examine the Sol translation-like Thales sphere, which we call Thaloid. We also discuss the behavior of this surface. In our work we will use the projective model of Sol described by E. Molnár in \cite{M97}. |
| title | Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry |
| topic | Metric Geometry 53A20, 53A35, 52C35, 53B20 |
| url | https://arxiv.org/abs/2405.05266 |