We study the limit geometry of complete projective special real manifolds. By limit geometry we mean the limit of the evolution of the defining polynomial and the centro-affine fundamental form along certain curves that leave every compact subset of the initial complete projective special real manifold. We obtain a list of possible limit geometries, which are themselves complete projective special real manifolds, and find a lower bound for the dimension of their respective symmetry groups. We further show that if the initial manifold has regular boundary behaviour, every possible limit geometry is isomorphic to $\mathbb{ R}_{ >0}\ltimes\mathbb{ R}^{ n-1}$.
Categories: math.DG hep-th math.AG