On the mappings preserving the hyperbolic polygons of type B together with their hyperbolic areas. (English) Zbl 1474.51015
Summary: In this paper, we present new characterizations of Möbius transformations and conjugate Möbius transformations by using the mappings preserving the hyperbolic polygons of type B together with their hyperbolic areas.
MSC:
| 51M10 | Hyperbolic and elliptic geometries (general) and generalizations |
| 30F45 | Conformal metrics (hyperbolic, Poincaré, distance functions) |
| 51B10 | Möbius geometries |
| 51M09 | Elementary problems in hyperbolic and elliptic geometries |
| 51M25 | Length, area and volume in real or complex geometry |
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