The λ -Point Map between Two Legendre Plane Curves

Azeb Alghanemi () and Abeer AlGhawazi
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Azeb Alghanemi: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Abeer AlGhawazi: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 4, 1-9

Abstract: The λ -point map between two Legendre plane curves, which is a map from the plane into the plane, is introduced. The singularity of this map is studied through this paper and many known plane map singularities are realized as special cases of this construction. Precisely, the corank one and corank two singularities of the λ -point map between two Legendre plane curves are investigated and the geometric conditions for this map to have corank one singularities, such as fold, cusp, swallowtail, lips, and beaks are obtained. Additionally, the geometric conditions for the λ -point map to have a sharksfin singularity, which is a corank two singularity, are obtained.

Keywords: Legendre curve; singularity; cusp; fold; swallowtail; slips; beaks; sharksfin (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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