PARALLEL LINEAR WEINGARTEN SURFACES IN E3 AND E3-1

PARALLEL LINEAR WEINGARTEN SURFACES IN E3 AND E3-1

In this paper we show that M is a linear Weingarten surface ifand only if Mris a linear Weingarten surface in E3and E3. And also wedetermine the types of the pair (M, M) according to the distance r

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  • Hacısaliho˘glu, H. H., Diferensiyel Geometri, In¨on¨u ¨Universitesi Fen-Edeb. Fak.Yayınları, 1983.
  • Lopez, R., Rotational Linear Weingarten Surfaces of Hyperbolic Type, Israel Journal of Math- ematics (2008), 167, 283-301.
  • Lopez, R., Kalkan, ¨O.B.and Sa˘glam, D., Non-degenerate Surfaces of Revolution in Minkowski Space That Satisfy the Relation aH + bK = c, Acta Math. Univ. Comenianae (2011), Vol. 80, 2, 201-212.
  • G¨org¨ul¨u, A.and C¸ ¨oken, A. C., The Dupin indicatrix for Parallel Pseudo-Euclidean Hyper- surfaces in Pseudo-Euclidean Space in Semi-Euclidean Space Rn+1, Journ. Inst. Math. and 1 Comp. Sci. (Math Series) 7 (1994), no.3, 221-225.
  • O’Neill, B. Semi-Riemannian Geometry With Applications To Relativity, Academic Press, New York, London, 1983.
  • Sa˘glam, D. and Kalkan, ¨O.B., Surfaces at a Constant Distance From the Edge of Regression on a Surface in E3, Differential Geometry-Dynamical Systems (2010), Vol. 12, 187-200.
  • Gray, A.,Modern Differential Geometry of Curves and Surfaces with Mathematica, 2000. Ankara University, Faculty of Science, Department of Mathematics, Ankara/TURKEY E-mail address: yayli@science.ankara.edu.tr Afyonkarahisar Kocatepe University, Faculty of Art and Sciences, Department of
  • Mathematics, Afyonkarahisar/TURKEY E-mail address: dryilmaz@aku.edu.tr E-mail address: bozgur@aku.edu.tr