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Journal of Geometry

, Volume 107, Issue 1, pp 137–149 | Cite as

Inversion with respect to a hypercycle of a hyperbolic plane of positive curvature

  • Lyudmila N. RomakinaEmail author
Article
  • 82 Downloads

Abstract

Inversion with respect to a hypercycle of a hyperbolic plane \({\widehat{H}}\) of positive curvature is investigated. The plane \({\widehat{H}}\) is the projective Cayley–Klein model of two-dimensional de Sitter’s space. One of four analogs of a Euclidean circle on the plane \({\widehat{H}}\) is a hypercycle. The formulae of inversion with respect to the hypercycle in a canonical frame of the first type are derived. The main properties of this inversion are proved.

Keywords

Hyperbolic plane \({\widehat{H}}\) of positive curvature hypercycle horizon of the hypercycle inversion with respect to a hypercycle of the hyperbolic plane \({\widehat{H}}\) of positive curvature 

Mathematics Subject Classification

Primary 51F05 Secondary 97G50 

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Copyright information

© Springer Basel AG 2015

Authors and Affiliations

  1. 1.EngelsRussia

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