Limit geometry of complete projective special real manifolds

Abstract

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 $\mathbb{R}_{>0}\ltimes\mathbb{R}^{n-1}$.