Acknowledgement
The authors would like to express their deep gratitude to the anonymous referee(s) and the editor of this esteemed journal for their valuable suggestions and constructive comments, which will resulted in the subsequent improvement of this research article.
References
- H. S. Abdel-Aziz, A study of tube-like surfaces according to type 2 Bishop frame in Euclidean space, Stud. Univ. Babes-Bolyai Math. 62 (2017), no. 2, 249-259. https://doi.org/10.24193/subbmath.2017.2.10
- H. S. Abdel-Aziz and M. Khalifa Saad, Weingarten timelike tube surfaces around a spacelike curve, Int. J. Math. Anal. (Ruse) 5 (2011), no. 25-28, 1225-1236.
- C. Baikoussis and T. Koufogiorgos, On the inner curvature of the second fundamental form of helicoidal surfaces, Arch. Math. (Basel) 68 (1997), no. 2, 169-176. https://doi.org/10.1007/s000130050046
- M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18 (2013), no. 1, 209-217.
- B. Divjak and Milin Sipus, Minding isometries of ruled surfaces in pseudo-Galilean space, J. Geom. 77 (2003), no. 1-2, 35-47. https://doi.org/10.1007/s00022-003-1646-6
- A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, second edition, CRC Press, Boca Raton, FL, 1998.
- I. Kamenarovic, Existence theorems for ruled surfaces in the Galilean space G3, Rad Hrvat. Akad. Znan. Umjet. No. 456 (1991), 183-196.
- M. K. Karacan and Y. Yayli, On the geodesics of tubular surfaces in Minkowski 3-space, Bull. Malays. Math. Sci. Soc. (2) 31 (2008), no. 1, 1-10.
- Z. M. Sipus, Ruled Weingarten surfaces in the Galilean space, Period. Math. Hungar. 56 (2008), no. 2, 213-225. https://doi.org/10.1007/s10998-008-6213-6
- B. O'Neill, Elementary Differential Geometry, Academic Press, New York, 1966.
- B. J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space G3, Glas. Mat. Ser. III 22(42) (1987), no. 2, 449-457.
- O. Roschel, Die Geometrie des Galileischen Raumes, Berichte, 256, Forschungszentrum Graz, Mathematisch, 1985.
- A. H. Sorour, Weingarten tube-like surfaces in Euclidean 3-space, Stud. Univ. Babes-Bolyai Math. 61 (2016), no. 2, 239-250.
- J. S. Ro and D. W. Yoon, Tubes of Weingarten types in a Euclidean 3-Space, J. Chungcheong Math. Soc. 22 (2009), 359-366.
- Z. Xu, R. Feng, and J. Sun, Analytic and algebraic properties of canal surfaces, J. Comput. Appl. Math. 195 (2006), no. 1-2, 220-228. https://doi.org/10.1016/j.cam.2005.08.002
- I. M. Yaglom, A simple non-Euclidean geometry and its physical basis, translated from the Russian by Abe Shenitzer, Springer-Verlag, New York, 1979.
- B. Yildiz, K. Arslan, H. Yildiz, and C. Ozgur, A geometric description of the ascending colon of some domestic animals, Ann Anat Anat Anzeiger 183 (2001), no. 6, 555-557. https://doi.org/10.1016/S0940-9602(01)80067-4
- S. Yilmaz, Construction of Frenet-Serret frame of a curve in 4D Galilean space and some applications, Int. Phys. Sci. 8 (2010), 1284-1289.