The Most General Planar Transformations That Map Parabolas into Parabolas

  title={The Most General Planar Transformations That Map Parabolas into Parabolas},
  author={Michael Bolt and TIMOTHY FERDINANDS and LANDON KAVLIE},
  • Published 2008
Consider the space of vertical parabolas in the plane interpreted generally to include nonvertical lines. It is proved that an injective map from a closed region bounded by one such parabola into the plane that maps vertical parabolas to other vertical parabolas must be the composition of a Laguerre transformation with a non-isotropic dilation. Here, a Laguerre transformation refers to a linear fractional or antilinear fractional transformation of the underlying dual plane. 

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