تقرير
New lower bound for the optimal congruent geodesic ball packing density of screw motion groups in $\mathbf{H}^2\!\times\!\mathbf{R}$ space
| العنوان: | New lower bound for the optimal congruent geodesic ball packing density of screw motion groups in $\mathbf{H}^2\!\times\!\mathbf{R}$ space |
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| المؤلفون: | Yahya, Arnasli, Szirmai, Jenő |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 52C17, 52C22, 53A35, 51M20 |
| الوصف: | In this paper, we present a new record for the densest geodesic congruent ball packing configurations in $\mathbf{H}^2\!\times\!\mathbf{R}$ geometry, generated by screw motion groups. These groups are derived from the direct product of rotational groups on $\mathbf{H}^2$ and some translation components on the real fibre direction $\mathbf{R}$ that can be determined by the corresponding Frobenius congruences. Moreover, we developed a procedure to determine the optimal radius for the densest geodesic ball packing configurations related to the considered screw motion groups. The highest packing density, $\approx0.80529$, is achieved by a multi-transitive case given by rotational parameters $(2,20,4)$. E. Moln\'{a}r demonstrated that homogeneous 3-spaces can be uniformly interpreted in the projective 3-sphere $\mathcal{PS}^3(\mathbf{V}^4, \boldsymbol{V}_4, \mathbf{R})$. We use this projective model of $\mathbf{H}^2\!\times\!\mathbf{R}$ to compute and visualize the locally optimal geodesic ball arrangements. Comment: 27 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2311.12260 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.21251 |
| رقم الأكسشن: | edsarx.2407.21251 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |