Position Vectors of the Natural Mate and Conjugate of a Space Curve
The concept of the natural mate and the conjugate curves associated to a smooth curve in Euclidian 3-space were introduced initially by Dashmukh and others. In this paper, we give some extra results that add more properties of the natural mate and the conjugate curves associated with a smooth space...
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/7565988 |
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| _version_ | 1832547380569833472 |
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| author | Azeb Alghanemi Meraj Ali Khan |
| author_facet | Azeb Alghanemi Meraj Ali Khan |
| author_sort | Azeb Alghanemi |
| collection | DOAJ |
| description | The concept of the natural mate and the conjugate curves associated to a smooth curve in Euclidian 3-space were introduced initially by Dashmukh and others. In this paper, we give some extra results that add more properties of the natural mate and the conjugate curves associated with a smooth space curve in E3. The position vectors of the natural mate and the conjugate of a given smooth curve are investigated. Also, using the position vector of the natural mate, the necessary and sufficient condition for a smooth given curve to be a Bertrand curve is introduced. Moreover, a new characterization of a general helix is introduced. |
| format | Article |
| id | doaj-art-ac22148cfb7546f9897698da94b70c92 |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-ac22148cfb7546f9897698da94b70c922025-02-03T06:45:10ZengWileyAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/7565988Position Vectors of the Natural Mate and Conjugate of a Space CurveAzeb Alghanemi0Meraj Ali Khan1Department of MathematicsDepartment of Mathematics and StatisticsThe concept of the natural mate and the conjugate curves associated to a smooth curve in Euclidian 3-space were introduced initially by Dashmukh and others. In this paper, we give some extra results that add more properties of the natural mate and the conjugate curves associated with a smooth space curve in E3. The position vectors of the natural mate and the conjugate of a given smooth curve are investigated. Also, using the position vector of the natural mate, the necessary and sufficient condition for a smooth given curve to be a Bertrand curve is introduced. Moreover, a new characterization of a general helix is introduced.http://dx.doi.org/10.1155/2023/7565988 |
| spellingShingle | Azeb Alghanemi Meraj Ali Khan Position Vectors of the Natural Mate and Conjugate of a Space Curve Advances in Mathematical Physics |
| title | Position Vectors of the Natural Mate and Conjugate of a Space Curve |
| title_full | Position Vectors of the Natural Mate and Conjugate of a Space Curve |
| title_fullStr | Position Vectors of the Natural Mate and Conjugate of a Space Curve |
| title_full_unstemmed | Position Vectors of the Natural Mate and Conjugate of a Space Curve |
| title_short | Position Vectors of the Natural Mate and Conjugate of a Space Curve |
| title_sort | position vectors of the natural mate and conjugate of a space curve |
| url | http://dx.doi.org/10.1155/2023/7565988 |
| work_keys_str_mv | AT azebalghanemi positionvectorsofthenaturalmateandconjugateofaspacecurve AT merajalikhan positionvectorsofthenaturalmateandconjugateofaspacecurve |