ON CERTAIN SPACE CURVES DUE TO PARALLEL TRANSPORT FRAME IN E^n

Charan Singh, Ahmet Kazan, Mustafa Altin, Sema Kazan, Mohammed Jamali

DOI Number
https://doi.org/10.22190/FUMI240411029S
First page
387
Last page
397

Abstract


In this paper, we study k-type (k\in{0,1,2,...,n-1}) slant helices due to non-zero parallel transport frame in E^n. We give some characterizations for 0-type, 1-type,..., and in general (n-1)-type slant helix due to parallel transport frame in terms of parallel transport curvatures in E^n and with the aid of these characterizations we give an important general theorem which gives the necessary and sufficient condition for any space curve to be k-type slant helices due to parallel transport frame in E^n. We also obtain the characterizations of the curves whose position vectors belong to the normal, rectifying and osculating spaces (called normal, rectifying and osculating curves, respectively) due to parallel transport frame in E^n.


Keywords

parallel transport frame, k-type slant helix, normal curve, rectifying curve, osculating curve.

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References


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DOI: https://doi.org/10.22190/FUMI240411029S

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