Geodesics and Visual boundary of Horospherical Products

Tom Ferragut (1)

1 Département de Mathématiques [Fribourg]

We study the geometry of horospherical products by providing a description of their distances, geodesics and visual boundary. These products contains both discrete and continuous examples, including Cayley graphs of lamplighter groups and solvable Lie groups of the form IR semi-direct product with (N1 ×N2), where N1 and N2 are two simply connected, nilpotent Lie groups.

Mots clés: Horocyclic product; Horospherical product; Gromov Hyperbolicity; Busemann space; Geodesic; Visual boundary; Solvable Lie groups

Domaines: Géométrie métrique [math.MG]; Théorie des groupes [math.GR]

Tom Ferragut. Geodesics and Visual boundary of Horospherical Products. 2022. ⟨hal-02933134v2⟩