3 papers
math.DG2021
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…
math.DG2020
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…
math.DG2019
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…