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Rubio cubics and generalized Cundy–Parry mappings

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Abstract

Rubio’s mappings between the Thomson and Darboux cubics are generalized for pairs of cubics of the form p α(β 2−γ 2)+ q β(γ 2−α 2)+ r γ(α 2 − β 2) = 0, where p, r, q, α, β, γ are functions of a triple (a, b, c) of variables or indeterminates. Methods include symbolic substitutions, such as (a, b, c) → (bc, ca, ab). Connections between the generalized Rubio mappings with generalized Cundy–Parry mappings are described.

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  1. Department of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, IN, 47722, USA

    Clark Kimberling

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  1. Clark Kimberling
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Correspondence to Clark Kimberling.

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Kimberling, C. Rubio cubics and generalized Cundy–Parry mappings. J. Geom. 96, 93–110 (2009). https://doi.org/10.1007/s00022-010-0025-3

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  • DOI: https://doi.org/10.1007/s00022-010-0025-3

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