Position Vectors of the Natural Mate and Conjugate of a Space Curve

Azeb Alghanemi and Meraj Ali Khan

Advances in Mathematical Physics, 2023, vol. 2023, issue 1

Abstract: 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.

Date: 2023
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https://doi.org/10.1155/2023/7565988

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:7565988

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