### SURFACE FAMILY WITH COMMON LINE OF CURVATURE IN 3-DIMENSIONAL GALILEAN SPACE

**DOI Number**

**First page**

**Last page**

#### Abstract

In this paper we study to find parametric presentation of a surface family with common line of curvature in 3-dimensional Galilean space. We obtain necessary and sufficient conditions for the curve to be a common line of curvature on this surface. We state examples to visualize our results and we obtain some results for a torsion free curve.

#### Keywords

#### Full Text:

PDF#### References

G.S¸ . Atalay and E. Kasap, Family of surface with a common null geodesic, International Journal of Physical Sciences 4(8) (2009) 428-433.

G.S¸ . Atalay and E. Kasap, Surfaces family with common null asymptotic, Applied Mathematics and Computation 260 (2015) 135-139.

M.E. Aydın, M.A. Külahc¸ı and A.O. öğrenmiş¸ Constant Curvature Translation Surfaces in Galilean 3-Space, International Electronic Journal of Geometry 12(1) (2019) 9-19.

W. Che, J-C. Paul and X. Zhang, Lines of curvature and umbilical points for implicit surfaces,Computer Aided Geometric Design 24(7) (2007) 395-409.

M. Dede, Tubular surfaces in Galilean space, Mathematical Communications 18(1) (2013)209-217.

B. Divjak, Z. Milin-Sipus, Special curves on ruled surfaces in Galilean and pseudo-Galilean space, Acta Math. Hungar.,98 (2003) 203-215.

E. Ergün, E. Bayram, and E. Kasap Surface pencil with a common line of curvature in Minkowski 3-space, Acta Mathematica Sinica, English Series 30.12 (2014) 2103-2118.

E. Ergün, E. Bayram, and E. Kasap, Surface family with a common natural line of curvature lift, Journal of Science and Arts 15(4) (2015) 321.

E. Kasap and F.T. Akyildiz, Surfaces with common geodesic in Minkowski 3-space, Applied mathematics and computation 177(1) (2006) 260-270.

E. Kasap, F.T. Akyildiz and K. Orbay, A generalization of surfaces family with common spatial geodesic, Applied Mathematics and Computation 201(1-2) (2008) 781-789.

C-Y. Li, R-H. Wang and C-G Zhu, Parametric representation of a surface pencil with a common line of curvature, Computer-Aided Design 43(9) (2011) 1110-1117.

C-Y. Li, R-H. Wang, and C-G Zhu, A generalization of surface family with common line of curvature, Applied Mathematics and Computation 219(17) (2013) 9500-9507.

C-Y. Li, R-H. Wang, and C-G Zhu, Designing approximation minimal parametric surfaces with geodesics. Applied mathematical modelling, 37(9) (2013) 6415-6424.

Z.E. Musielak and J. L. Fry. Physical theories in Galilean space-time and the origin of Schr¨odinger-like equations, Annals of Physics 324.2 (2009) 296-308.

A.O. Öğrenmis, M. Ergut and M. Bektas, On the helices in the Galilean space G3, Iran.J. Sci. Technol. Trans. A Sci. 31(2) (2007) 177-181.

A.O. Öğrenmiş, H. Öztekin and M. Ergüt, Bertrand curves in Galilean space and their characterizations, Kragujevac Journal of Mathematics 32(32) (2009) 139-147.

H. Öztekin, Special Bertrand curves in 4D Galilean space, Mathematical Problems in Engineering, (2014).

O. Röschel, Die geometrie des Galileischen raumes, Forschungszentrum Graz, Mathematisch-Statistische Sektion, Graz, 1(2) (1985).

D.J. Struik, Lectures on classical differential geometry. Courier Corporation (1961). [20] I.M. Yaglom, 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, (2012).

D.W. Yoon, J.W. Lee and C.W. Lee, Osculating curves in the Galilean 4-Space, International Journal of Pure and Applied Mathematics 100(4) (2015) 497-506.

D.W. Yoon and Z.K. Y¨uzbasi, An approach for hypersurface family with common geodesic curve in the 4d galilean space G3, The Pure and Applied Mathematics 25(4) (2018) 229-241.

Z.K. Yüzbaşı and M. Bektaş, On the construction of a surface family with common geodesic in Galilean space G3, Open Physics 14(1) (2016) 360-363.

Z.K. Yüzbası, On a family of surfaces with common asymptotic curve in the Galilean space G3, J. Nonlinear Sci. Appl 9 (2016) 518-523.

G-J. Wang, K. Tang and C-L. Tai, Parametric representation of a surface pencil with a common spatial geodesic, Computer-Aided Design 36(5) (2004) 447-459.

DOI: https://doi.org/10.22190/FUMI2005315A

### Refbacks

- There are currently no refbacks.

ISSN 0352-9665 (Print)