Straight projective-metric spaces with centres
It is proved that a straight projective-metric space has an open set of centres, if and only if it is either the hyperbolic or a Minkowskian geometry. It is also shown that if a straight projective-metric space has some finitely many well-placed centres, then it is either the hyperbolic or a Minkowskian geometry.
KeywordsProjective-metric Central symmetry Minkowski geometry Hilbert geometry
Mathematics Subject Classification51F99 53A35 52A20
- 4.C̆ap, A., Cowling, M.G., de Mari, F., Eastwood, M., McCallum, R.: The Heisenberg Group, SL(3, R), and Rigidity, Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory, Lecture Notes Series, Institute of Mathematical Sciences, National University of Singapore, vol. 12. World Scientific, New Jersey–London (2007)Google Scholar