When the differentiable curve, used throughoutthis 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.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this paper, we investigate the conditions of being an harmonic curve and research differential equations characterizing any differentiable curve in Euclidean 3-space.
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Temel Bulgular & Veri:By means of the Laplacian image of the meancurvature vector field of a curve, it is stated which type of harmonic the curve is.
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Sonuç & Katkı:When the differentiable curve, used throughoutthis 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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
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 meancurvature vector field of a curve, it is stated which type of harmonic the curve is. Then we write the theorems relatedto the characterization of the curves and proved these theorems. When the differentiable curve, used throughoutthis 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.
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Bu Makaleye Atıf Yap
Şenyurt, S., Çakır, O. (2022). Characterizations of Curves According to Frenet Frame in Euclidean 3-Space. Turkish Journal of Mathematics and Computer Science, Cilt: 11 - Sayı: 1, 48–52. https://ajindex.com/articles/609120
Arslan, K., Kocayigit, H., Onder, M., Characterizations of Space Curves with 1-type Darboux Instantaneous Rotation Vector, Commun. Korean Math. Soc., 31(2)(2016), 379–388
Chen, B. Y., Ishikawa, S., Biharmonic Surface in Pseudo-Euclidean Spaces, Mem. Fac. Sci. Kyushu Univ., A45(1991), 323–347
Hacısalihoglu, H. H. Diferensiyel Geometri 3rd ed., Ankara, 1988
Kocayigit, H., Hacisalihoglu H. H., 1-type Curves and Biharmonic Curves in Euclidean 3-Space, Int. Elect. Journ. of Geo., 4(1)(2011), 97–101
Kocayigit, H., Hacısalihoğlu, Hilmi H., Biharmonic Curves in Contact Geometry, Commun. Fac. Sci. Univ. Ank. Series A1, 2061(2)(2012), 35-43
Kocayigit, H., Onder, M., Hacisalihoglu H. H., Harmonic 1-type Curves and Weak Biharmonic Curves in Lorentzian 3-Space, Ana. Stiin. A. Uni. Al. I. Cuza. D. I. (S.N.) Mat., f(1)(2014), 109–124
Sabuncuoglu, A., Diferensiyel Geometri 5 th ed., Ankara, 2014
S¸ enyurt, S., C¸ akır O., Diferential Equations for a Space Curve According to the Unit Darboux Vector, Turk. J. Math. Comput. Sci., 9(2018), 91–97.