English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

After having investigated several types of geodesic ball packings in $\SXR$space, in this paper we study the locally optimal geodesic simply and multiplytransitive ball packings with equal balls to the space groups generated byrotations in $\HXR$ geometry which space can be derived by the direct productof the hyperbolic plane $\bH^2$ and the real line $\bR$.  Moreover, we develop a procedure to determine the densities of the abovelocally densest geodesic ball packing configurations. Additionally, we examinethe monotonicity properties of the densities within infinite series of theconsidered space groups.  E. Moln\'ar showed, that the homogeneous 3-spaces have a unifiedinterpretation in the projective 3-sphere $\mathcal{PS}^3(\bV^4,\BV_4,\mathbf{R})$. In our work, we use this projective model of $\HXR$ and applythis to the visualization of locally optimal ball arrangements.

Geodesic ball packings generated by rotations and monotonicity behavior of their densities in $\mathbf{H}^2\!\times\!\mathbf{R}$ space