The <i>λ</i>-Point Map between Two Legendre Plane Curves
The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-point map between two Legendre plane curves, which is a map from the plane into the plan...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/997 |
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| author | Azeb Alghanemi Abeer AlGhawazi |
| author_facet | Azeb Alghanemi Abeer AlGhawazi |
| author_sort | Azeb Alghanemi |
| collection | DOAJ |
| description | The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-point map to have a sharksfin singularity, which is a corank two singularity, are obtained. |
| first_indexed | 2024-03-11T08:28:00Z |
| format | Article |
| id | doaj.art-08c6c62203f2429b8acb948da808bcad |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:00Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-08c6c62203f2429b8acb948da808bcad2023-11-16T21:56:55ZengMDPI AGMathematics2227-73902023-02-0111499710.3390/math11040997The <i>λ</i>-Point Map between Two Legendre Plane CurvesAzeb Alghanemi0Abeer AlGhawazi1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThe <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula>-point map to have a sharksfin singularity, which is a corank two singularity, are obtained.https://www.mdpi.com/2227-7390/11/4/997Legendre curvesingularitycuspfoldswallowtailslips |
| spellingShingle | Azeb Alghanemi Abeer AlGhawazi The <i>λ</i>-Point Map between Two Legendre Plane Curves Mathematics Legendre curve singularity cusp fold swallowtail slips |
| title | The <i>λ</i>-Point Map between Two Legendre Plane Curves |
| title_full | The <i>λ</i>-Point Map between Two Legendre Plane Curves |
| title_fullStr | The <i>λ</i>-Point Map between Two Legendre Plane Curves |
| title_full_unstemmed | The <i>λ</i>-Point Map between Two Legendre Plane Curves |
| title_short | The <i>λ</i>-Point Map between Two Legendre Plane Curves |
| title_sort | i λ i point map between two legendre plane curves |
| topic | Legendre curve singularity cusp fold swallowtail slips |
| url | https://www.mdpi.com/2227-7390/11/4/997 |
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