Using the Izumiya and Takeuchi’s paper as an inspiration, Bertrand curves of Finslerianspherical curves are defined according to Randers metric which is a special Finslerian metric.Also, we obtain the Finsler helix derived from the Finslerian circle according to Randers metricand their visualizations are given by using the Mathematica program.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this study, we give the linear condition for the Bertrand curve of a given curve in Finslerian 3-space.
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Temel Bulgular & Veri:In this study, we give the linear condition for the Bertrand curve of a given curve in Finslerian 3-space.
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Sonuç & Katkı:Using the Izumiya and Takeuchi’s paper as an inspiration, Bertrand curves of Finslerianspherical curves are defined according to Randers metric which is a special Finslerian metric.Also, we obtain the Finsler helix derived from the Finslerian circle according to Randers metricand their visualizations are given by using the Mathematica program.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
In this study, we give the linear condition for the Bertrand curve of a given curve in Finslerian 3-space. Using the Izumiya and Takeuchi’s paper as an inspiration, Bertrand curves of Finslerianspherical curves are defined according to Randers metric which is a special Finslerian metric.Also, we obtain the Finsler helix derived from the Finslerian circle according to Randers metricand their visualizations are given by using the Mathematica program.
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Bu Makaleye Atıf Yap
OZDEMIR, Z., ATES, F., EKMEKCI, F. N. (2022). Characterizations of Bertrand Curves in Finsler 3-Manifold. Gazi University Journal of Science, Cilt: 33 - Sayı: 3, 726–735. https://ajindex.com/articles/521259
Akbar-Zadeh, H., “Initiation to global Finslerian geometry”, North-Holland Math Library, (2006).
Asanjarani, A., Bidabad, B., "Classification of complete Finsler manifolds through a second order differential equation", Differential Geometry and its Applications, 26: 434-444, (2008).
Bejancu, A., Farran, H.R., “Geometry of pseudo-Finsler submanifolds”, Kluwer Academic Publishers, (2000).
Shen, Z., “Lecture on Finsler geometry”, World Scientific Publishing Company, (2001).
Ergut, M., Kulahci M., "Special curves in three dimensional Finsler manifold 𝐹3 ", TWMS Journal of Pure and Applied Mathematics, (5)2: 147-151, (2014).
Remizov, A.O., "Geodesics in generalized Finsler spaces: singularities in dimension two", Journal of Singularities, 14: 172-193, (2016).
Yildirim, M.Y., Bektas, M., "Helices of the 3-dimensional Finsler manifold", Journal of Advanced Mathematical Studies, 2(1): 107-113, (2009).
Yildirim, M.Y., "Biharmonic general helices in 3 −dimensional Finsler manifold", Karaelmas Science and Engineering Journal, 7(1): 1-4, (2017).
Randers, G., "On an asymmetric metric in the four-space of general relativity", Physical Review Journals, 59: 195-199, (1941).
Bertrand, J.M., "Memoire sur la theorie des courbes a double courbure", Journal de Mathematiques Pures et Appliquees, 15: 332-350, (1850). Izumiya, S., Takeuchi, N., “Generic properties of helices and Bertrand curves”, Journal of Geometry, 74: 97-109, (2002).
Babaarslan, M., “Constant slope surfaces and their applications”, P.hD. thesis, Ankara University, (2013).
Tamassy, L., "Direct geometrical method in Finsler geometry", Variations, Geometry and Physics, (17): 293-314, (2009).
Chern, S.S., Shen, Z., “Riemann Finsler Geometry”, World Scientific, (2005).
Ates, F., Ozdemir, Z., Ekmekci, N., "Special curves in Finsler space", Proceedings of the Institute of Mathematics and Mechanics, 44(2): 198-208, (2018).