Ceva's and Menelaus' theorems characterize the hyperbolic geometry among Hilbert geometries

DOI10.1007/s00022-014-0258-7zbMath1457.53007OpenAlexW2093250126MaRDI QIDQ895712

Árpád Kurusa, József Kozma

Publication date: 4 December 2015

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-014-0258-7

zbMATH Keywords

classificationhyperbolic geometryHilbert geometryCeva's theoremMenelaus' theorem

Mathematics Subject Classification ID

Non-Euclidean differential geometry (53A35) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Elementary problems in hyperbolic and elliptic geometries (51M09)

Related Items (3)

Hyperbolic is the only Hilbert geometry having circumcenter or orthocenter generally ⋮ Ceva's and Menelaus' theorems in projective-metric spaces ⋮ Unnamed Item

Cites Work

• A characterization of hyperbolic geometry among Hilbert geometry
• An arithmetic proof of John's ellipsoid theorem
• Convex and Discrete Geometry
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Ceva's and Menelaus' theorems characterize the hyperbolic geometry among Hilbert geometries