Characterizations of tzitzeica curves using FLC frame

ŞENYURT, Süleyman; EREN, Kemal; AYVACI, Kebire Hilal

doi:10.14744/sigma.2024.00005

Süleyman ŞENYURT ¹

, Kemal EREN ²

, Kebire Hilal AYVACI ¹

¹Department of Mathematics, Faculty of Arts and Science, Ordu University, Ordu, 52200, Türkiye
²Department of Mathematics, Faculty of Arts and Science, Sakarya University, Sakarya, 54050, Türkiye

Sigma J Eng Nat Sci 2024; 42(1): 37-41 DOI: 10.14744/sigma.2024.00005

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Abstract

In this study, we investigate the condition that a given polynomial curve with respect to the Frenet like curve (Flc) frame is a Tzitzeica curve. We also show that any planar polynomial curve cannot be a Tzitzeica curve. Finally, the condition to be the Tzitzeica curve for each of the spherical indicatrix curves defined according to the Flc frame is expressed, separately.

Keywords: Polynomial Curves; Tzitzeica Curve; FLC Frame; Spherical Indicatrix