Convexes divisibles IV : Structure du bord en dimension 3 |
| |
Authors: | Yves Benoist |
| |
Institution: | (1) Ecole Normale Supérieure-CNRS, 45 rue d’Ulm, 75230 Paris, France |
| |
Abstract: | Divisible convex sets IV: Boundary structure in dimension 3
Let Ω be an indecomposable properly convex open subset of the real projective 3-space which is divisible i.e. for which there exists a torsion free discrete group Γ of projective transformations preserving Ω such that the quotient
M := Γ\Ω is compact. We study the structure of M and of ∂Ω, when Ω is not strictly convex:
The union of the properly embedded triangles in Ω projects in M onto an union of finitely many disjoint tori and Klein bottles which induces an atoroidal decomposition of M.
Every non extremal point of ∂Ω is on an edge of a unique properly embedded triangle in Ω and the set of vertices of these
triangles is dense in the boundary of Ω (see Figs. 1 to 4).
Moreover, we construct examples of such divisible convex open sets Ω.
|
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|