Parametric Represantations of Surfaces Containing a Common Isophote Curve In 3-Dimensional Galilean Space
DOI:
https://doi.org/10.30605/proximal.v9i1.7851Keywords:
the isophote curve, the non-isophote curve, the isophote asymtotic curve, Galilean 3-spaceAbstract
This paper investigates a family of defined surfaces that share a common isophote curve in three‑dimensional Galilean space. By employing a given curve in this space with its Frenet frame we derive characterizations of the surfaces and present illustrative examples where in the curve functions, as an isophote.
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Doğan, F., Yayli, Y. (2015). On isophote curves and their characterizations. Turkish Journal, of Mathematics, 39(5), 650-664.
Koenderink, J. J., van Doorn, A. J. (1980). Photometric invariants related to solid shape. Optic Acta: International Journal of Optics, 27(7), 981-996.
Poeschl, T. (1984). Detecting surface irregularities using isophotes. Computer Aided Geometric Design, 1(2), 163-168.
Sara, R. Local Shading Analysis via Isophotes Properties. PhD, Johannes Kepler University, Austria, 1994.
Kim, K. J., Lee, I. K. (2003). Computing isophotos of surface of revolution and canal surface. Computer-aided design, 35(3), 215-223.
Izumiya, S., & Takeuchi, N. (2004). New special curves and developable surfaces. Turkish Journal of Mathematics, 28(2), 153-164.
Dogan, F. (2012). Isophote curves on timelike surfaces in Minkowski 3-space. arXiv preprint arXiv:1203.4389.
Ergün, E., Bayram, E., & Kasap, E. (2014). Surface pencil with a common line of curvature in Minkowski 3-space. Acta Mathematica Sinica, English Series, 30(12), 2103-2118.
Ergün, E., Bayram, E., & Kasap, E. (2015). Surface family with a common natural line of curvature lift. Journal of Science and Arts, 15(4), 321.
Yaglom, I. M. (2012). A simple non-Euclidean geometry and its physical basis: An elementary account of Galilean geometry and the Galilean principle of relativity. Springer Science & Business Media.
Musielak, Z. E., Fry, J. L. (2009). Physical theories in Galilean space-time and the origin of Schrödinger-like equations. Annals of Physics, 324(2), 296-308.
Aydın, M. E., Külahçı, M. A., & Öğrenmiş, A. O. (2019). Constant curvature surfaces in Galilean 3-space. International Electronic Journal of Geometry, 12(1), 9-19.
Dede, M. (2013). Tubular surfaces in Galilean space. Mathematical Communications, 18(1), 209-217.
Divjak, B., & Milin-Šipuš, Z. (2002). Special curves on ruled surfaces in Galilean and pseudo- Galilean spaces. Acta Mathematica Hungarica, 98(3), 203-215.
Yoon, D. W., Lee, J. W., & Lee, C. W. (2015). Osculating curves in the Galilean 4- space. International Journal of Pure and Applied Mathematics, 100(4), 497-506.
Yoon, D. W., Yüzbaşi, Z. K., & Bektaş, M. (2017). An approach for surfaces using an asymptotic curve in Lie Group. Journal of Advanced Physics, 6(4), 586-590.
Yüzbası, Z. K. (2016). On a family of surfaces with common asymptotic curve in the Galilean space G^3. J. Nonlinear Sci. Appl, 9, 518-523.
Ali, A. T., & Turgut, M. (2019). Some characterizations of isophote curves on surfaces. Mathematics and Computers in Simulation, 155, 196–206.
Celik, Y., & Onder, M. (2020). Special curves and surfaces in Galilean and pseudo-Galilean spaces. Applied Mathematics and Computation, 372, 124991.
Ersoy, S., & Tosun, M. (2021). Isophote curves according to the Darboux frame. Journal of Geometry, 112(2), 1–15.
Körpınar, T., & Demir, E. (2018). On isophote curves and surfaces in non-Euclidean spaces. Advances in Applied Clifford Algebras, 28(3), 1–14.
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Copyright (c) 2026 ŞEYDA ÖZEL, Mehmet Bektaş

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