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Geodesics and visual boundary of horospherical products
[Géodésiques et bord visuel des produits horosphériques]
Tom Ferragut1
1IUT de Vannes, 8 Rue Michel de Montaigne, 56000 Vannes, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 2, pp. 351-406

We study the geometry of horospherical products by providing a description of their distances, geodesics and visual boundary. These products contain both discrete and continuous examples, including Cayley graphs of lamplighter groups and solvable Lie groups of the form $\mathbb{R}\ltimes (N_1\times N_2)$, where $N_1$ and $N_2$ are two simply connected, nilpotent Lie groups.

Nous étudions la géométrie des produits horosphériques en fournissant une description de leurs distances, de leurs géodésiques et de leur bord visuel. Ces produits incluent à la fois des exemples discrets et continus, notamment les graphes de Cayley des groupes lamplighter ainsi que certains groupes de Lie résolubles de la forme $\mathbb{R}\ltimes (N_1\times N_2)$, où $N_1$ et $N_2$ sont deux groupes de Lie nilpotents, simplement connexes.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1849
Classification : 20F65, 20F67, 22E25
Keywords: metric geometry, hyperbolic spaces, horospherical products, solvable groups, geodesics
Mots-clés : géométrie métrique, espaces hyperboliques, produits horosphériques, groupes résolubles, géodésiques

Tom Ferragut  1

1 IUT de Vannes, 8 Rue Michel de Montaigne, 56000 Vannes, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Tom Ferragut. Geodesics and visual boundary of horospherical products. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 2, pp. 351-406. doi: 10.5802/afst.1849
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