Envelopes of slant lines in the hyperbolic plane

Authors

  • Takashi Ashino
  • Hisayoshi Ichiwara
  • Shyuichi Izumiya

DOI:

https://doi.org/10.1285/i15900932v35n2p51

Keywords:

slant geometry, Hyperbolic plane, horocycles, equidistant curves

Abstract

In this paper we consider envelopes of families of equidistant curves and horocycles in the hyperbolic plane. As a special case, we consider a kind of evolutes as the envelope of normal equidistant families of a curve. The hyperbolic evolute of a curve is a special case. Moreover, a new notion of horocyclic evolutes of curves is induced. We investigate the singularities of such envelopes and introduce new invariants in the Lie algebra of the Lorentz group.

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Published

04-04-2016

Issue

Volume 35, Issue 2 (2015)

Section

Articoli

License

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Gli autori che pubblicano in questa rivista accettano i termini e le condizioni specificate nella licenza Creative Commons di cui al link sottostante.

http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode