TY  - JOUR
T1  - Some Singularities and Developable Surfaces in Galilean 3-Space
AU  - Demir Çetin, Esma
AU  - Gülücü, Ümit
PY  - 2025
DA  - April
Y2  - 2025
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 161
EP  - 169
VL  - 18
IS  - 1
LA  - en
AB  - In this work we investigate singularities for the three types of developable surfaces, introduced by Izumiya and Takeuchi, in Galilean-3 space. Moreover we search thenecessary conditions of being a geodesic for principal direction curves of the rectifying developable surface.
KW  - Singular points
KW  - developable surfaces
KW  - Galilean space
CR  - Ali, A.T.: Position vectors of curves in the Galilean space G3. Matematicki Vesnik. 64(3),200-210 (2012).
CR  - Ali, A.T. and Lopez, R.: Slant helices in Minkowski 3-space. J. Korean Math. Soc. 48/1, 159–167 (2011).
CR  - Aydın, M. E., Külahçı, M. A. and Ö˘grenmi¸s , A. O.: Constant curvature translation surfaces in Galilean 3-space. Int. Electronic J. of Geometry. 12 (1), 9-19 (2019).
CR  - Brander, D.: Singularities of spacelike constant mean curvature surfaces in Lorentz- Minkowski space. Cambridge Philosophical Society Mathematical Proceedings. 150, 527–556 (2011).
CR  - Divjak, B. and Sipus, Z.: Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces . Acta Math. Hungar. 98(3), 203-215 (2003).
CR  - Fujimori, S., Saji, K., Umehara, M. and Yamada, K.: Singularities of maximal surfaces. Math. Z. 259, 827–848 (2008).
CR  - Ishikawa, G. and Yamashita, T.: Singularities of tangent surfaces to directed curves. Topology and its Applications. 234, 198–208 (2018).
CR  - Izumiya, S. and Takeuchi, N.: New special curves and developable surfaces. Turk J. Math. 28, 153–163 (2004).
CR  - Izumiya, S., Katsumi, H. and Yamasaki, T.: The rectifying developable and the spherical Darboux image of a space curve. Geometry and Topology of Caustics-Caustics ’98-Banach Center Publications. 137–149 (1999).
CR  - Karacan, M. K. and Tunçer, Y.: Characterizations of slant helix in Galilean and pseudo-Galilean spaces. SAÜ Fen Edebiyat Dergisi. 82, 279–316 (2009).
CR  - Kokubu, M., Rossman, W., Saji, K., Umehara, M. and Yamada, K.: Singularities of flat fronts in hyperbolic space. Pacific J. Math. 221, 303–351 (2005).
CR  - Murata, S. and Umehara, S.:Flat surfaces with singularities in Euclidean 3-space. J. Differential Geometry. 82, 279–316 (2009).
CR  - Öğrenmi¸s, A.O., Ergüt, M. and Bekta¸s, M.: On The helices in the Galilean space G3 . Iranian J. Sci. Tech. Transaction A. Vol. 31(A2), 177-181 (2007).
CR  - Sipus, Z. and Divjak, B.: Translation surfaces in the Galilean space. Glasnik Matematicki. 46(66), 455-469 (2011).
CR  - Zhao, Q., Pei, D. and Wang, Y.: Singularities for one-parameter developable surfaces of curves. Symmetry. 11/108, 153–163(2019).
UR  - https://dergipark.org.tr/en/pub/iejg/issue//1587696
L1  - https://dergipark.org.tr/en/download/article-file/4377116
ER  -