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Envelopes of slant lines in the hyperbolic plane


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.

DOI Code: 10.1285/i15900932v35n2p51

Keywords: slant geometry; Hyperbolic plane; horocycles; equidistant curves

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