Dae Won Yoon, zuhal kucukarslan yuzbasi

DOI Number
First page
Last page


In this paper, our aim is to give surfaces in the Galilean 3-space G3 with the property that there exist four geodesics through each point such that every surface built with the normal lines and the binormal lines along these geodesics is a surface with a minimal surface and a constant negative Gaussian curvature. We show that should be an isoparametric surface in G3: A plane or a circular hyperboloid.


surfaces, Galilean 3-space, geodesics

Full Text:



M. Barros, General helices and a theorem of Lancret, Proc. Amer. Math. Soc. 125, (1997), 1503-1509.

M. Dede, C. Ekici and A. C. Coken, On the parallel surfaces in Galilean space. Hacet. J. Math. Stat. 42, (2013), 605-615.

M Dede and C Ekici, On parallel ruled surfaces in Galilean space. Kragujevac J. Math. 40, (2016), 47-59

W. Kuhnel, Differential Geometry: Curves - Surfaces - Manifolds. Wiesdaden: Braunchweig, 1999.

R. Lopez and G. Ruiz-Hernandez, A Characterization of Isoparametric Surfaces in R3 Via Normal Surfaces. Results Math. 67(1-2), (2015), 87-94.

E. Molnar, The projective interpretation of the eight 3-dimensional Homogeneous geometries. Beitr. Algebra Geom. 38, (1997), 261-288.

B. J. Pavkovic and I. Kamenarovic, The Equiform differential geometry of curves in the Galilean space G3. Glas. Mat. 22(42) (1987), 449-457.

O. Roschel, Die Geometrie des Galileischen raumes. Habilitationsschrift, Leoben, 1984.

E. Salkowski, Zur transformation von raumkurven. Math. Ann. 66, (1909), 517-557.

Z. M. Sipus, Ruled Weingarten surfaces in Galilean space. Period. Math. Hungvol, 56(2), (2008), 213-225.

Z. M. Sipus and B. Divjak, Surfaces of constant curvature in the pseudo-Galilean space. International J. Math. Math. Sci. 2012 (2012), 1-28.

T. Sahin, Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space. Acta Math. Sci. 33(3), (2013), 701-711.

M. Tamura, Surfaces which contain helical geodesics. Geom. Dedicata, 42, (1992), 311-315.

M. Tamura, A differential geometric characterization of circular cylinders. J. Geom. 52, (1995), 189-192.

I. M. Yaglom, A simple non-Euclidean geometry and its physical basis. Springer-Verlag: New York Inc, 1979.



  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)