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Real projective structures on $n$-orbifolds are useful in understanding thespace of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolicmanifolds deform to manifolds with such structures not projectively equivalentto the original ones. The purpose of this paper is to understand the structuresof ends of real projective $n$-dimensional orbifolds. In particular, these havethe radial or totally geodesic ends. In previous papers, we classified properlyconvex or complete radial ends under suitable conditions. In this paper, wewill study radial ends that are convex but not properly convex nor completeaffine. The main techniques are the theory of Fried and Goldman on affinemanifolds, and a generalization of the work on Riemannian foliations by Molino,Carri\`ere, and so on. We will show that these are quasi-joins of horospheresand totally geodesic radial ends. These are deformations of joins ofhorospheres and totally geodesic radial ends.

A classification of radial and totally geodesic ends of properly convex  real projective orbifolds III: the convex but nonproperly convex and  non-complete-affine radial ends