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Real projective structures on $n$-orbifolds are useful in understanding thespace of representations of discrete groups into $SL(n+1, \mathbb{R})$ or$PGL(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifoldsdeform to manifolds with such structures not projectively equivalent to theoriginal ones. The purpose of this paper is to understand the structures ofends of real projective $n$-dimensional orbifolds. In particular, these havethe radial or totally geodesic ends. Hyperbolic manifolds with cusps andhyper-ideal ends are examples. For this, we will study the natural conditionson eigenvalues of holonomy representations of ends when these ends aremanageably understandable. The main techniques are the theory of Fried andGoldman on affine manifolds, a generalization of the work of Goldman, Labourie,and Margulis on flat Lorentzian $3$-manifolds and the work on Riemannianfoliations by Molino, Carri\`ere, and so on. We will show that only the radialor totally geodesic ends of lens type or horospherical ends exist for stronglyirreducible properly convex real projective orbifolds under the suitableconditions.

A classification of radial and totally geodesic ends of properly convex real projective orbifolds