ON MEUSNIER THEOREM FOR PARALLEL SURFACES

Year 2017, Volume: 66 Issue: 1, 187 - 198, 01.02.2017

Ziya Ümit Savcı Ali Görgülü Cumali Ekici

https://doi.org/10.1501/Commua1_0000000788

Cited By: 1

https://izlik.org/JA53JG27CM

Abstract

In this paper, the geodesic curvature, the normal curvature, thegeodesic torsion and the curvature of the image curve on a parallel surfaceof a given curve on a surface are obtained. Moreover, Meusnier theorem forparallel surfaces are discussed

Keywords

Parallel surface , geodesic curvature , normal curvature , geodesic torsion , Meusnier theorem

References

• W. Blaschke, Diferensiyel Geometri Dersleri, ·Istanbul Üniversitesi Yay. No. 433, 1949.
• L. Brand, Vector and Tensor Analysis, John Wiley & Sons Inc., 1948.
• T. Craig, Note on parallel surfaces, Journal Für Die Reine und Angewandte Mathematik (Crelle’s Journal), 94 (1883), 162-170.
• A. C. Çöken, Ü. Çiftci, and C. Ekici, On parallel timelike ruled surfaces with timelike rulings, Kuwait Journal of Science & Engineering, 35 (2008), 21-31.
• L.P. Eisenhart, A Treatise on the Diğ erential Geometry of Curves and Surfaces, Boston: New York [etc.] Ginn and Company, 1909.
• A. Görgülü, A. C. Çöken, The Dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space En+1, Journ. Inst. Math. and Comp. Sci. (Math. Series) 7(3), (1994), 221-225.
• A. Görgülü, A. C. Çöken, The Euler theorem for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space En+1, Journ. Inst. Math. and Comp. Sci. (Math. Series) 6(2), (1993), 165.
• H. H. Hacısaliho¼glu, Diferensiyel Geometri, ·Inönü Ünv. Fen Edebiyat Fak. Yayınları, No.2, S. Kızıltu¼g, Ö. Tarakcı, Y. Yaylı, On the Curves Lying on Parallel Surfaces in the Euclidean space E3, Journal of Advanced Research in Dynamical and Control Systems, 5(3), (2013), 35.
• E. Kreyszig, Diğ erential Geometry, Dover Publications, Inc.,1991.
• ¸S. Nizamoglu, Surfaces Réglées Parallèles, Ege Üniv. Fen Fak. Derg., 9A, (1986), 37-48.
• B. O’Neill, Elementary Diğ erential Geometry, Acedemic Press, Inc., 1966.
• M. Önder, S. Kızıltu¼g, Bertrand and Mannheim Partner D-Curves on Parallel Surfaces in Minkowski 3-Space, Internatıonal journal of Geometry, 1(2), (2012), 34-45.
• K. R. Park, G. I. Kim, Oğ sets of ruled surfaces, J. Korean Computer Graphics Society, 4, (1998), 69-75.
• A. Sabuncuo¼glu, Diferensiyel Geometri, Nobel Yayın Da¼gıtım, 2001.
• D. W. Yoon, Some properties of parallel surfaces in Euclidean 3-spaces, Honam Mathematical J., 30(4), (2008), 637-644.
• Dirk J. Struik, Lectures on Classical Diğ erential Geometry, Dover Publications, Inc., 1961.
• Current address : ÜM ·IT Z·IYA SAVCI: Celal Bayar University, Department of Mathematics Education , 45900, Manisa, TURKEY