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2009 The most general planar transformations that map parabolas into parabolas
Michael Bolt, Timothy Ferdinands, Landon Kavlie
Involve 2(1): 79-88 (2009). DOI: 10.2140/involve.2009.2.79

Abstract

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 nonisotropic dilation. Here, a Laguerre transformation refers to a linear fractional or antilinear fractional transformation of the underlying dual plane.

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Michael Bolt. Timothy Ferdinands. Landon Kavlie. "The most general planar transformations that map parabolas into parabolas." Involve 2 (1) 79 - 88, 2009. https://doi.org/10.2140/involve.2009.2.79

Information

Received: 5 September 2008; Accepted: 11 February 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1171.51001
MathSciNet: MR2501346
Digital Object Identifier: 10.2140/involve.2009.2.79

Subjects:
Primary: 51B15

Rights: Copyright © 2009 Mathematical Sciences Publishers

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