TY - JOUR TT - Parallel Surfaces of Spacelike Ruled Weingarten Surfaces in AU - Ünlütürk, Yasin AU - Ekici, Cumali PY - 2013 DA - April JF - New Trends in Mathematical Sciences PB - Mustafa BAYRAM WT - DergiPark SN - 2147-5520 SP - 85 EP - 92 VL - 1 IS - 1 KW - Spacelike Weingarten surface KW - parallel surface KW - spacelike ruled Weingarten surface KW - curvatures N2 - In this work, it is shown that parallel surfaces of spacelike ruled surfaces which are developable are spacelike ruled Weingarten surfaces. It is also shown that parallel surfaces of non-developable ruled Weingarten surfaces are again Weingarten surfaces. Finally, some properties of that kind parallel surfaces are obtained in Minkowski 3-space CR - Beltrami, E., Risoluzione di un problema relativo alla teoria delle supercie gobbe, Ann. Mat. Pura Appl., 7, 139-150., 1865. CR - Brunt, B., Weingarten surfaces design and application of curves and surfaces, Fisher, R., (Ed.), Mathematics of surfaces V, Oxford Univ. Press., 1994. CR - Brunt, B. and Grant, K., Potential applications of Weingarten surfaces in CAGD. I: Weingarten surfaces and surface shape investigation, Comput. Aided Geom. Des., 13, 569-582., 1996. CR - Dillen, F. and Kühnel, W., Ruled Weingarten surfaces in Minkowski 3-space, Manuscripta Math., 98, 307-320., 1999. CR - Dillen, F. and Sodsiri, W., Ruled surfaces of Weingarten type in Minkowski 3-space, J. Geom., 83, 10-21., 2005. CR - Dillen, F. and Sodsiri, W., Ruled surfaces of Weingarten type in Minkowski 3-space-II, J. Geom., 84, 37-44., 2005. CR - Dini, U., Sulle super.cie gobbe nelle quali uno dei due raggidi curvatura principale e una funzione dellaltro, Ann. Mat. Pura Appl., 7, 205-210.,1865. CR - Görgülü, A. and Çöken, C., The Dupin indicatrix for parallel pseudo-Euclidean hypersurfaces in pseudo-Euclidean space in CR - Journ. Inst. Math. and Comp. Sci. (Math Series), 7(3), 221-225., 1994. CR - semi-Euclidean space CR - Gray, A., Modern differential geometry of curves and surfaces, CRC Press, Inc., 1993. CR - Hou, Z. H. and Ji, F., Helicoidal surfaces with CR - Kim, M. H. and Yoon, D. W., Weingarten quadric surfaces in a Euclidean 3-space, Turk. J. Math. 34, 1-7., 2010. CR - Koch, R., Die Weingarten-regelflächen, J. Geom. 47, 77-85., 1993. CR - Kühnel, W., Ruled W-surfaces, Arch. Math. (Basel), 62, 475-480., 1994. CR - Lopez, R., Di¤erential geometry of curves and surfaces in Lorentz-Minkowski space, Mini-Course taught at the Instituto de Matematica e Estatistica (IME-USP), University of Sao Paulo, Brasil, 2008. CR - O’Neill, B., Semi Riemannian geometry with applications to relativity, Academic Press, Inc. New York, 1983. CR - Turgut, A. and Hacısalihoğlu, H. H., Spacelike ruled surfaces in the Minkowski 3-space, Commun. Fac. Sci. Univ. Ank. Series A1, v. 46, pp. 83-91, 1997. CR - Unluturk, Y., and Ekici, C., On spacelike parallel ruled surfaces in Minkowski 3-space, (Preprint). CR - Unluturk, Y., Ekici, C., and Özüsağlam, E., On parallel surfaces in Minkowski 3-space, (Preprint). CR - Weingarten, J., Über eine klasse auf einander abwickelbarer .ächen, J. Reine Angew. Math. 59, 382-393, 1861. CR - Weingarten, J., Über eine flächen, derer normalen eine gegebene flächeberühren, Journal für die Reine und Angewandte Mathematik, 62, 61-63, 1863. CR - D. W. Yoon, Some properties of parallel surfaces in Euclidean 3-spaces, Honam Mathematical J. 30, No. 4, pp, 637-644, 2008. UR - https://dergipark.org.tr/tr/pub/ntims/issue//260166 L1 - https://dergipark.org.tr/tr/download/article-file/226648 ER -