N. V. Abrosimov, L. A. Mikaiylova, “Casey's theorem in hyperbolic geometry”, Sib. Èlektron. Mat. Izv., 2015, Volume 12,Pages <nobr>354

This article is cited in 5 papers

Geometry and topology

Casey's theorem in hyperbolic geometry

N. V. Abrosimov^abc, L. A. Mikaiylova^a

^a Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia
^b Laboratory of Quantum Topology, Chelyabinsk State University, Brat’ev Kashirinykh st., 129, 454001, Chelyabinsk, Russia
^c Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We obtain a hyperbolic version of Casey's theorem. A similar result is obtained in spherical geometry as well.

Keywords: Casey's theorem, Ptolemy's theorem, hyperbolic plane, spherical plane.

UDC: 514.13

MSC: 51M09

Received May 26, 2015, published June 9, 2015

Language: English

DOI: 10.17377/semi.2015.12.029