2 citations · 2 across the 6 of their papers we have counts for
6 papers
Affine three-manifolds with centralizing holonomy
Raphaël V Alexandre
According to the Markus conjecture, closed flat affine manifolds with parallel volume should be complete. We show it is the case for three-manifolds when the holonomy centralizes a…
Closed ray nil-affine manifolds and parabolic geometries
Raphaël Alexandre
Ray nil-affine geometries are defined on nilpotent spaces. They occur in every parabolic geometry and in those cases, the nilpotent space is an open dense subset of the correspondi…
Closed ray affine manifolds
Raphaël Alexandre
We consider closed manifolds that possess a so called rank one ray structure. That is a (flat) affine structure such that the linear part is given by the products of a diagonal tra…
Redundancy of triangle groups in spherical CR representations
Raphaël Alexandre
Falbel, Koseleff and Rouillier computed a large number of boundary unipotent CR representations of fundamental groups of non compact three-manifolds. Those representations are not…
Geodesic convexity and closed nilpotent similarity manifolds
Raphaël Alexandre
Some nilpotent Lie groups possess a transformation group analogous to the similarity group acting on the Euclidean space. We call such a pair a nilpotent similarity structure. It i…
Fried's theorem for boundary geometries of rank one symmetric spaces
Raphaël Alexandre
After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifo…