Image Curves on the Parallel-like Surfaces in E³

Year 2023, , 122 - 131, 30.04.2023

Semra Yurttançıkmaz , Ömer Tarakcı

https://doi.org/10.36890/iejg.1178434

Cited By: 1

Abstract

In this paper, it's introduced the curves lying on parallel-like surface M^{f} of a surface M in Euclidean space. Taking into account the definition of the parallel-like surface it's obtained parametric expression of these curves and examined the Darboux frame for these curves which we call image curves. And finally, the curves lying on the surfaces M and M^{f} are compared by considering their geodesic and normal curvatures, the geodesic torsion.

Keywords

Darboux frame, parallel-like surfaces, image curves

References

• [1] Çakmak, A., Tarakcı, Ö.: The Image Curves on Surfaces at a Constant Distance from the edge of regression on a surface of revolution. International Journal of Mathematics and Computation. 1, 74-85 (2016).
• [2] Çakmak, A.: Surfaces at a Constant Distance from the Edge of Regression on a Surface of Revolution in E3. Applied Mathematical Sciences, 10(15), 707 -719 (2016). http://dx.doi.org/10.12988/ams.2016.53222
• [3] Gray, A., Abbena E., Salamon S.: Modern Differential Geometry of Curves and Surfaces with Mathematica (Third Edition). Studies in Advanced Mathematics. (2006). https://doi.org/10.1201/9781315276038
• [4] Kızıltuğ, S., Tarakcı Ö., Yaylı Y.: On the curves lying on parallel surfaces in the Euclidean 3-space E3. Journal of Advanced Research in Dynamical and Control Systems. 5(3), 26-35 (2013).
• [5] Kızıltuğ, S., Yaylı Y.: Timelike Curves on Timelike Parallel Surfaces in Minkowski 3-Space $E^3_1$. Mathematica Aeterna. 2(8), 689-700 (2012).
• [6] Kuhnel, W.: Differential Geometry Curves-Surfaces-Manifolds. American Mathematical Society. Wiesbaden Braunchweig (1999).
• [7] Önder, M., Kızıltuğ S.: Bertrand and Manheim Partner D-Curves On Parallel Surfaces in Minkowski 3-Space. Int. Journal of Geometry. 1(2), 34-45 (2012).
• [8] Özkaldı, S., Yaylı Y.: Constant Angle Surfaces And Curves in E3. International Electronic Journal of Geometry. 4(1), 70-78 (2011).
• [9] Sabuncuoğlu, A.: Differential Geometry. Nobel Publications. Ankara (2006).
• [10] Sağlam, D., Kalkan Ö.: Surfaces at a Constant Distance From the Edge of Regression on a Surface in $E^3_1$ . Differential Geometry-DynamicalSystems. 12, 187-200 (2010).
• [11] Tarakcı, Ö.: Surfaces At a Constant Distance From The Edge of Regression On a Surface. PhD thesis. Ankara University (2002).
• [12] Tarakcı, Ö., Hacısaliho˘ glu, H.H.: Surfaces At a Constant Distance From The Edge of Regression On a Surface. Applied Mathematics and Computation. 155(1), 81-93 (2004). https://doi.org/10.1016/S0096-3003(03)00761-6
• [13] Yurttançıkmaz, S., Tarakcı, Ö.: The Relationship between Focal Surfaces and Surfaces at a Constant Distance from the Edge of Regression on a Surface. Advances in Mathematical Physics. Article ID 397126, 1-6 (2015). https://doi.org/10.1155/2015/397126
• [14] Yurttançıkmaz, S.: On The Parallel-Like Surfaces. PhD thesis. Atatürk University (2016).