تقرير
Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry
العنوان: | Interior angle sums of geodesic triangles and translation-like isoptic surfaces in Sol geometry |
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المؤلفون: | Csima, Géza, Szirmai, Jenő |
سنة النشر: | 2024 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Metric Geometry, 53A20, 53A35, 52C35, 53B20 |
الوصف: | 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 $\pi$. 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. Moln\'ar in \cite{M97}. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2405.05266 |
رقم الأكسشن: | edsarx.2405.05266 |
قاعدة البيانات: | arXiv |
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