Tubular Surfaces with Galilean Darboux Frame in G3
DOI:
https://doi.org/10.15407/mag15.02.278Ключові слова:
трубчаста поверхня, галілеєвий репер Дарбу, геодезична лінія, асимптотична лінія, простір Галілея.Анотація
Суть цього дослідження полягає у вивченні нового підходу до визначення трубчастих поверхонь з галілеєвим репером Дарбу у тривимірному просторі Галілея. Отримано також гаусову та середню кривизни і виведено параметризацію для спеціальної кривої, що лежить на трубчастих поверхнях з галілеєвим репером Дарбу.
Mathematics Subject Classification: 53A35, 53Z05.
Посилання
A.T. Ali, Position vectors of curves in the Galilean space G3 , Mat. Vesnik 64 (2012), No. 3, 200–210.
A. Artykbaev, Reconstruction of convex surfaces for the extrinsic curvature in a Galileian space, Mat. Sb. (N.S.) 119(161) (1982), No. 2, 204–224 (Russian).
M. Dede, Tubular surfaces in Galilean space, Math. Commun. 18(1) (2013), 209– 217.
M. Dede, C. Ekici, W. Goemans, and Y. Ünlütürk, Twisted surfaces with vanishing curvature in Galilean 3-space, Int. J. Geom. Methods Mod. Phys. 15 (2018), No. 1, 1850001. https://doi.org/10.1142/S0219887818500019
F. Doğan and Y. Yaylı, Tubes with Darboux frame, Int. J. Contemp. Math. Sci. 7 (2012), 751–758.
F. Doğan and Y. Yaylı, On the curvatures of Tubular surface with Bishop frame, Commun. Fac. Sci. Univ. Ank. Ser. A 60 (2011), 59–69. https://doi.org/10.1501/Commua1_0000000669
M.K. Karacan and Y. Tuncer, Tubular surfaces of Weingarten types in Galilean and pseudo-Galilean, Bull. Math. Anal. Appl. 5 (2013), 87–100.
S. Kızıltuğ and Y. Yaylı, Timelike tubes with Darboux frame in Minkowski 3-space, Int. J. Phys. Sci. 8 (2013), 31–36. https://doi.org/10.5897/IJPS12.602
J. Lang and O. Röschel, Developable (1, n)-Bezier surfaces, Comput. Aided Geom. Design 9 (1992), 291–298. https://doi.org/10.1016/0167-8396(92)90036-O
T. Maekawa, M. N. Patrikalakis, T. Sakkalis, and G. Yu, Analysis and applications of pipe surfaces, Comput. Aided Geom. Design 15 (1998), 437–458. https://doi.org/10.1016/S0167-8396(97)00042-3
E. Molnár, The projective interpretation of the eight 3-dimensional homogeneous geometries, Beiträge Algebra Geom. 38 (1997), 261–288.
A.O. Öğrenmis, H. Öztekin, and M. Ergüt, Bertrand curves in Galilean space and their characterizations, Kragujevac J. Math. 32 (2009), 139–147.
B.J. Pavković and I. Kamenarović, The Equiform differential geometry of curves in the Galilean space G3 , Glas. Mat. Ser. III 22(42) (1987), 449–457.
J.S. Ro and D.W. Yoon, Tubes of Weingarten types in a Euclidean 3-space, J. Chungcheong Math. Soci. 22(3) (2009), 359–366.
B.A. Rosenfeld, A history of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space, Springer Science + Business Media, New York, 2012.
O. Röschel, Die Geometrie des Galileischen Raumes, Bericht der MathematischStatistischen Sektion in der Forschungs-Gesellschaft Joanneum, Bericht Nr. 256, Habilitationsschrift, Leoben, 1984.
Z. Milin-Šipuš, Ruled Weingarten surfaces in Galilean space, Period. Math. Hungar 56(2) (2008), 213–225. https://doi.org/10.1007/s10998-008-6213-6
Z. Milin-Šipuš and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space, Int. J. Math. Math. Sci. 2012 (2012), Art. ID 375264. https://doi.org/10.1155/2012/375264
T. Şahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Math. Sci. Ser. B 33 (2013), 701–711. https://doi.org/10.1016/S0252-9602(13)60031-4
I.M. Yaglom, A Simple Non-Euclidean Geometry and its Physical Basis, SpringerVerlag, New York-Heidelberg, 1979.
D.W. Yoon, On the Gauss map of tubular surfaces in Galilean 3-space, Int. J. Math. Anal. (N.S.) 8 (2014), No. 45, 2229–2238. https://doi.org/10.12988/ijma.2014.4365
Z.K. Yüzbaşı and M. Bektaş, On the construction of a surface family with common geodesic in Galilean space G3 , Open Phys. 14 (2016), 360–363. https://doi.org/10.1515/phys-2016-0041
