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    STUDIA MATHEMATICA - Issue no. 3 / 2015  
         
  Article:   CURVES WITH CONSTANT GEODESIC CURVATURE IN THE BOLYAI-LOBACHEVSKIAN PLANE.

Authors:  .
 
       
         
  Abstract:  The aim of this note is to present the curves with constant geodesic curvature of the Bolyai-Lobachevskian hyperbolic plane. By using the Lobachevskian metric the equations of the circle, paracycloid and hipercycloid are given. Furthermore, we determine a new family of curves with constant curvature which was not emphasized before. During the analysis we use Cartesian and polar coordinates.

Mathematics Subject Classification (2010): 53A35.

Keywords: hyperbolic geometry, geodesics, orthogonal trajectory, polar coordinates.
 
         
     
         
         
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