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## Characterizations of Curves According to Frenet Frame in Euclidean 3-Space

#### Osman Çakır [1] , Süleyman Şenyurt [2]

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In this paper, we investigate the conditions of being an harmonic curve and research differential equations characterizing any differentiable curve in Euclidean 3-space. By means of the Laplacian image of the mean curvature vector field of a curve, it is stated which type of harmonic the curve is. Then we write the theorems related to the characterization of the curves and proved these theorems. When the differentiable curve, used throughout this paper, is specifically  replaced to the unit speed curve then it is seen that the results coincide with the study [4].   In addition we elucidate the characterizations of helix as an example.
regular curve, connection, mean curvature, biharmonic, differential equation
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Primary Language en Mathematics Articles Orcid: 0000-0002-2664-5232Author: Osman Çakır Orcid: 0000-0003-1097-5541Author: Süleyman Şenyurt (Primary Author)Institution: Ordu ÜniversitesiCountry: Turkey Publication Date: June 30, 2019
 Bibtex @research article { tjmcs526778, journal = {Turkish Journal of Mathematics and Computer Science}, issn = {}, eissn = {2148-1830}, address = {Matematikçiler Derneği}, year = {2019}, volume = {11}, pages = {48 - 52}, doi = {}, title = {Characterizations of Curves According to Frenet Frame in Euclidean 3-Space}, key = {cite}, author = {Çakır, Osman and Şenyurt, Süleyman} } APA Çakır, O , Şenyurt, S . (2019). Characterizations of Curves According to Frenet Frame in Euclidean 3-Space. Turkish Journal of Mathematics and Computer Science, 11 (1), 48-52. Retrieved from http://dergipark.org.tr/tjmcs/issue/46614/526778 MLA Çakır, O , Şenyurt, S . "Characterizations of Curves According to Frenet Frame in Euclidean 3-Space". Turkish Journal of Mathematics and Computer Science 11 (2019): 48-52 Chicago Çakır, O , Şenyurt, S . "Characterizations of Curves According to Frenet Frame in Euclidean 3-Space". Turkish Journal of Mathematics and Computer Science 11 (2019): 48-52 RIS TY - JOUR T1 - Characterizations of Curves According to Frenet Frame in Euclidean 3-Space AU - Osman Çakır , Süleyman Şenyurt Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics and Computer Science JF - Journal JO - JOR SP - 48 EP - 52 VL - 11 IS - 1 SN - -2148-1830 M3 - UR - Y2 - 2019 ER - EndNote %0 Turkish Journal of Mathematics and Computer Science Characterizations of Curves According to Frenet Frame in Euclidean 3-Space %A Osman Çakır , Süleyman Şenyurt %T Characterizations of Curves According to Frenet Frame in Euclidean 3-Space %D 2019 %J Turkish Journal of Mathematics and Computer Science %P -2148-1830 %V 11 %N 1 %R %U ISNAD Çakır, Osman , Şenyurt, Süleyman . "Characterizations of Curves According to Frenet Frame in Euclidean 3-Space". Turkish Journal of Mathematics and Computer Science 11 / 1 (June 2019): 48-52. AMA Çakır O , Şenyurt S . Characterizations of Curves According to Frenet Frame in Euclidean 3-Space. TJMCS. 2019; 11(1): 48-52. Vancouver Çakır O , Şenyurt S . Characterizations of Curves According to Frenet Frame in Euclidean 3-Space. Turkish Journal of Mathematics and Computer Science. 2019; 11(1): 52-48.