In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in terms of the size of the automorphism group and the regularity of the boundary.
"Characterizing the unit ball by its projective automorphism group." Geom. Topol. 20 (4) 2397 - 2432, 2016. https://doi.org/10.2140/gt.2016.20.2397