Some Special Types of Developable Ruled Surface ABSTRACT | FULL TEXT

Yıl 2010, Cilt: 39 Sayı: 3, - 6, 01.03.2010

P. Alegre K. Arslan A. Carriazo C. Murathan G. Öztürk

Anahtar Kelimeler

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Kaynakça

• Chen, B. Y. When does the position vector of a space curve always lie in its rectifying plane?, Am. Math Monthly 110, 147–152, 2003.
• Eisenhart, L. P. A Treatise on the Differential Geometry of Curves and Surfaces (Dover Pub. Inc., New York, 1909).
• Gluck, H. Higher curvatures of curves in Euclidean space, Am. Math. Monthly 73, 699–704, Gray, A. Modern Differential Geometry of Curves and Surfaces (CRC Press, Boca Raton, FL, ). Gursoy, O. Some results on closed ruled surfaces and closed space curves, Mech. Mach. Theory , 323–330, 1990.
• Hacısaliho˘glu, H. H. Diferensiyel Geometri (Gazi ¨Universitesi Basın-Yayın Y¨uksekokulu Basımevi, Ankara, 1983) (In Turkish).
• Izumiya, S. and Takeuchi, N. New special curves and developable surfaces, Turkish J. Math. 28, –163, 2004.
• Izumiya, S. and Takeuchi, N. Special curves and ruled surfaces, Cont. to Alg. and Geo. 44, –212, 2003.
• Izumiya, S. and Takeuchi, N. Geometry of Ruled Surfaces (Applicable mathematics in the Goldon Age (ed. J. C. Misra), 305–308, Narosa Pulishing House, New Delhi, 2003).
• Izumiya, S., Katsumi, H. and Yamashi, T. The rectifying developable and spherical Darboux image of a space curve, Geom. and Top. of caustics - Caustics’98 Banach Center Publications , 137–149, 1999.
• Koenderink, J. Solid Shape (MIT Press, Cambridge MA, 1990).
• Laugwitz, D. Differential and Riemannian Geometry (Academic Press, New York, 1965).
• Monterde, J. Curves with constant curvatures ratios, arXiv:math/0412323v1.
• Ozyilmaz, E. and Yayli, Y. On the closed space-like developable ruled surface, Hadronic J. 23 (4), –456, 2000.
• Uribe-Vargas, R. On vertices, focal curvatures and differential geometry of space curves, Bull. Brazilian Math. Soc. 36 (3), 285–307, 2005.