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The λ -Point Map between Two Legendre Plane Curves

Author

Listed:
  • 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
    Department of Mathematics, Al-Baha University, P.O. Box 1988, Al Bahah 65799, Saudi Arabia)

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.

Suggested Citation

  • Azeb Alghanemi & Abeer AlGhawazi, 2023. "The λ -Point Map between Two Legendre Plane Curves," Mathematics, MDPI, vol. 11(4), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:997-:d:1069865
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    References listed on IDEAS

    as
    1. Azeb Alghanemi & Abeer AlGhawazi & Meraj Ali Khan, 2022. "Some Geometric Characterizations of f-Curves Associated with a Plane Curve via Vector Fields," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-9, April.
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