Affine deformations of quasi‐divisible convex cones

We study subgroups of SL ( 3 , R ) ⋉ $\mathrm{SL}(3,\mathbb {R})\ltimes \mathbb {R}^3$ obtained by adding a translation part to the holonomy finite-volume convex projective surface. Under natural condition on translations added peripheral parabolic elements, we show that affine action group $\mathbb has domains discontinuity which are regular, generalizing result Mess for globally hyperbolic flat spacetimes. then classify all such arising from fixed and quotient each them is an manifold foliated surfaces with constant Gaussian curvature (CAGC). The proof based analysis CAGC developed in previous work, along correspondence between geometry space endowed cone tube domain. also moduli groups vector bundle over structures, rank equal dimension Teichmüller space.