ON THE PARALLEL SURFACES IN GALILEAN SPACE

Year 2013, Volume: 42 Issue: 6, 605 - 615, 01.06.2013

Mustafa Dede Cumali Ekici A. Ceylan Çöken

Abstract

In this paper, first of all, the definition of parallel surfaces in Galileanspace is given. Then, the relationship between the curvatures of theparallel surfaces in Galilean space is determined. Moreover, the firstand second fundamental forms of parallel surfaces are found in Galileanspace. Consequently, we obtained Gauss curvature and mean curvatureof parallel surface in terms of those curvatures of the base surface.

Keywords

Parallel surfaces, Surface curvature, Galilean space

ON THE PARALLEL SURFACES IN GALILEAN SPACE

Abstract

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Keywords

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References

• C ¸ ¨ oken, A. C., C ¸ ift¸ ci, ¨ U. and Ekici, C. On parallel timelike ruled surfaces with timelike rulings, Kuwait Journal of Science & Engineering, 35 (1A), 21–31, 2008.
• Dede, M. Tubular surfaces in Galilean space, Math. Commun., 18, 209–217, 2013.
• Divjak, B. Curves in pseudo-Galilean geometry, Annales Univ. Sci. Budapest, 41, 117–128, 199 Eisenhart, L. P. A treatise on the differential geometry of curves and surfaces, (Dover Publication, Inc., New York, 1960).
• Ekici, C. and Dede, M. On the Darboux vector of ruled surfaces in pseudo-Galilean space, Mathematical and Computational Applications, 16(4), 830–838, 2011.
• G¨ org¨ ul¨ u, A. and C ¸ ¨ oken A. C. The Euler theorem for parallel pseudo-Euclidean hpersurfaces in pseudo-Euclidean space E n+1 1 , Journ. Inst. Math. and Comp. Sci. (Math. Series), 6.2, 161–165, 1993.
• Guggenheimer, H. W. Differential geometry, (McGraw-Hill, New York, 1963).
• Kamenarovic, I. Existence theorems for ruled surfaces in the Galilean space G 3 , Rad Hrvatske Akad. Znan. Umj. Mat., 456(10), 183–196, 1991.
• Milin-Sipus, Z. Ruled Weingarten surfaces in Galilean space, Periodica Mathematica Hungarica, 56(2), 213–225, 2008.
• Milin-Sipus, Z. and Divjak, B. Special curves on ruled surfaces in Galilean and pseudoGalilean spaces, Acta Math. Hungar., 98(3), 203–215, 2003.
• ¨ O˘ grenmi¸ s, A., Erg¨ ut, M. and Bekta¸ s, M. On the helices in the Galilean space G 3 , Iranian Journal of Science & Technology, Transaction A, 31(A2), 177–181, 2007.
• Roberts, S. On Parallel surfaces, Proc. London Math. Soc., 1-4(1), 218–236, 1871.
• Roberts, S. On the parallel surfaces of developables and curves of double curvature, Proc. London Math. Soc., 1-5(1), 90–94, 1873.
• R¨ oschel, O. Die geometrie des Galileischen raumes, (Habilitationsschrift, Leoben, 1984). Sa˘ gel, M. K. and Hacısaliho˘ glu, H. H. On the parallel hypersurfaces with constant curvature, Commun. Fac. Sci. Univ. Ank. Series A, 40, 1–5, 1991.
• Yaglom, I. M. A simple non-Euclidean geometry and its physical basis, (Springer-Verlag, New York Inc., 1979).