On geometry of the parallel surface of the tube surface given by the Flc frame in Euclidean 3-space
Keywords:
Parallel surface, tubular surface, Flc frame, Gaussian transform.Abstract
In this study, first, the parallel surfaces of the tube surfaces given with the Flc frame are defined. By calculating the Gaussian and mean curvatures of these parallel surfaces, it was found the conditions developable and minimal. Afterwards, the conditions for parameter curves on the parallel surface to be asymptotic, geodesic and curvature lines were investigated. It has been proven that the tube and parallel tube surface preserve the Gaussian transform. Finally, examples of these surfaces are given.
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Published
2025-09-28
How to Cite
Ayvacı Şimşek, K. H., & Şenyurt, S. (2025). On geometry of the parallel surface of the tube surface given by the Flc frame in Euclidean 3-space. International Journal of Maps in Mathematics, 8(2), 653–667. Retrieved from https://simadp.com/journalmim/article/view/340
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