تقرير
Fibre-like cylinders, their packings and coverings in $\widetilde{\mathbf{S}\mathbf{L}_2\mathbf{R}}$ space
| العنوان: | Fibre-like cylinders, their packings and coverings in $\widetilde{\mathbf{S}\mathbf{L}_2\mathbf{R}}$ space |
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| المؤلفون: | Szirmai, Jenő |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 52C17, 52C22, 52B15, 53A35, 51M20 |
| الوصف: | In this paper we define the notion of infinite or bounded fibre-like geodesic cylinder in $\widetilde{\mathbf{S}\mathbf{L}_2\mathbf{R}}$ space, develop a method to determine its volume and total surface area. We prove that the common part of the above congruent fibre-like cylinders with the base plane are Euclidean circles and determine their radii. Using the former classified infinite or bounded congruent regular prism tilings with generating groups $\mathbf{pq2_1}$ we introduce the notions of cylinder packings, coverings and their densities. Moreover, we determine the densest packing, the thinnest covering cylinder arrangements in $\widetilde{\mathbf{S}\mathbf{L}_2\mathbf{R}}$ space, their densities, their connections with the extremal hyperbolic circle arrangements and with the extremal fibre-like cylinder arrangements in $\mathbf{H}X\mathbf{R}$ space In our work we use the projective model of $\widetilde{\mathbf{S}\mathbf{L}_2\mathbf{R}}$ introduced by E. Moln\'ar in \cite{M97}. Comment: 23 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1403.3192, arXiv:1304.0546 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2306.05721 |
| رقم الأكسشن: | edsarx.2306.05721 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |