تقرير
Translation-like isoptic surfaces and angle sums of translation triangles in $\NIL$ geometry
| العنوان: | Translation-like isoptic surfaces and angle sums of translation triangles in $\NIL$ geometry |
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| المؤلفون: | Csima, Géza, Szirmai, Jenő |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 53A20, 53A35, 52C35, 53B20 |
| الوصف: | After having investigated the geodesic and translation triangles and their angle sums in $\SOL$ and $\SLR$ geometries we consider the analogous problem in $\NIL$ space that is one of the eight 3-dimensional Thurston geometries. We analyze the interior angle sums of translation triangles in $\NIL$ geometry and we provide a new approach to prove that it can be larger than or equal to $\pi$. Moreover, for the first time in non-constant curvature Thurston geometries we have developed a procedure for determining the equations of $\NIL$ isoptic surfaces of translation-like segments and as a special case of this we examine the $\NIL$ translation-like Thales sphere, which we call {\it Thaloid}. In our work we will use the projective model of $\NIL$ described by E. Moln\'ar in \cite{M97}. Comment: 22 pages, 6 figures. arXiv admin note: text overlap with arXiv:1710.02394, arXiv:1703.06646 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.07653 |
| رقم الأكسشن: | edsarx.2302.07653 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |