Parallel surfaces with constant mean curvature in a Galilean 3-space

İsmet Gölgeleyen; Elif Yaren Bulgan; İsmet Gölgeleyen; Elif Yaren Bulgan

doi:10.3934/math.2026836

AIMS Mathematics

2026, Volume 11, Issue 7: 20558-20576. doi: 10.3934/math.2026836

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Research article

Parallel surfaces with constant mean curvature in a Galilean 3-space

İsmet Gölgeleyen ^{1
,
,},
Elif Yaren Bulgan ²

1.
Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, Zonguldak 67100, Türkiye
2.
Graduate School of Natural and Applied Sciences, Zonguldak Bülent Ecevit University, Zonguldak 67100, Türkiye

Received: 18 May 2026 Revised: 26 June 2026 Accepted: 02 July 2026 Published: 13 July 2026
MSC : 53A10, 53A35, 53B30

In this paper, we investigate the parallel surfaces of all three types of surfaces of revolution in the Galilean 3-space $ G^{3} $ under the condition that the mean curvature of the parallel surface is constant. For each type of revolution surface, we explicitly compute the mean curvature of the corresponding parallel surface and derive the ordinary differential equations governing the profile curves. By solving these equations, we obtain explicit expressions for the functions defining these surfaces. Furthermore, several representative examples are presented, and the resulting surfaces are visualized to illustrate the influence of the parallel surface transformation on the geometry of revolution surfaces in the Galilean setting.
- parallel surface,
- revolution surface,
- mean curvature,
- Galilean space
Citation: İsmet Gölgeleyen, Elif Yaren Bulgan. Parallel surfaces with constant mean curvature in a Galilean 3-space[J]. AIMS Mathematics, 2026, 11(7): 20558-20576. doi: 10.3934/math.2026836

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Abstract

In this paper, we investigate the parallel surfaces of all three types of surfaces of revolution in the Galilean 3-space $ G^{3} $ under the condition that the mean curvature of the parallel surface is constant. For each type of revolution surface, we explicitly compute the mean curvature of the corresponding parallel surface and derive the ordinary differential equations governing the profile curves. By solving these equations, we obtain explicit expressions for the functions defining these surfaces. Furthermore, several representative examples are presented, and the resulting surfaces are visualized to illustrate the influence of the parallel surface transformation on the geometry of revolution surfaces in the Galilean setting.

References

[1]	B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern geometry – Methods and applications: Part Ⅰ. The geometry of surfaces, transformation groups, and fields, New York: Springer, 1984. https://doi.org/10.1007/978-1-4684-9946-9
[2]	A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with mathematica, 3 Eds., New York: Chapman & Hall/CRC, 2006. https://doi.org/10.1201/9781315276038
[3]	A. T. Ali, Position vectors of curves in the Galilean space $G^{3}$, Mat. Vesn., 64 (2012), 200–210.
[4]	M. E. Aydın, M. A. Kulahçı, A. O. Öğrenmi ş, Constant curvature translation surfaces in Galilean 3-space, Int. Electron. J. Geom., 12 (2019), 9–19. https://doi.org/10.36890/iejg.545741 doi: 10.36890/iejg.545741
[5]	Z. M. Šipuš, Ruled Weingarten surfaces in Galilean space, Period. Math. Hung., 56 (2008), 213–225. https://doi.org/10.1007/s10998-008-6213-6 doi: 10.1007/s10998-008-6213-6
[6]	Ž. M. Šipuš, B. Divjak, Surfaces of constant curvature in the Pseudo-Galilean space, Int. J. Math. Math. Sci., 2012 (2012), 375264. https://doi.org/10.1155/2012/375264 doi: 10.1155/2012/375264
[7]	Y. Yaylı, I. Gölgeleyen, Minimal curves on ruled surfaces generated by Legendre curves, J. New Theory, 49 (2024), 43–52. https://doi.org/10.53570/jnt.1545097 doi: 10.53570/jnt.1545097
[8]	M. Dede, C. Ekici, W. Goemans, Surfaces of revolution with vanishing curvature in Galilean 3-space, J. Math. Phys. Anal. Geo., 14 (2018), 141–152. https://doi.org/10.15407/mag14.02.141 doi: 10.15407/mag14.02.141
[9]	İ. Gölgeleyen, Y. Yaylı, E. Y. Bulgan, Surfaces of revolution with constant mean curvature in Galilean 3-space, Mathematics, 14 (2026), 1066. https://doi.org/10.3390/math14061066 doi: 10.3390/math14061066
[10]	İ. Kişi, A new approach to revolution surface with its focal surface in the Galilean 3-space $G_{3}$, Hacet. J. Math. Stat., 50 (2021), 1722–1737. https://doi.org/10.15672/hujms.905636 doi: 10.15672/hujms.905636
[11]	D. W. Yoon, Surfaces of revolution in the three dimensional Pseudo-Galilean space, Glas. Mat., 48 (2013), 415–428. https://doi.org/10.3336/gm.48.2.13 doi: 10.3336/gm.48.2.13
[12]	M. Dede, C. Ekici, A. C. Çöken, On the parallel surfaces in the Galilean space, Hacet. J. Math. Stat., 42 (2013), 605–615.
[13]	İ. Gölgeleyen, Y. Yaylı, E. Y. Bulgan, Developable ruled surfaces with constant mean curvature along a curve , Mathematics, 14 (2026), 234. https://doi.org/10.3390/math14020234 doi: 10.3390/math14020234
[14]	S. Büyükkütük, I. Kişi, G. Öztü rk, E. Kişi, Parallel hypersurfaces in $E^{4}$ and their applications to rotational hypersurfaces, Mathematics, 13 (2025), 3684. https://doi.org/10.3390/math13223684 doi: 10.3390/math13223684
[15]	U. Dierkes, S. Hildebrandt, A. Küster, O. Wohlrab, Minimal surfaces I: Boundary value problems, Berlin, Heidelberg: Springer, 1992. https://doi.org/10.1007/978-3-662-02791-2
[16]	S. Adriaenssens, P. Block, D. Veenendaal, C. Williams, Shell structures for architecture: Form finding and optimization, London: Routledge, 2014. https://doi.org/10.4324/9781315849270
[17]	M. Dede, Tubular surfaces in Galilean space, Math. Commun., 18 (2013), 209–217.
[18]	O. Röschel, Die geometrie des galileischen raumes, Habilitationsschrift, Leoben, 1984.

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