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The aim of this paper is to study the Mannheim partner curves in Euclidean space E 3. We obtain the relationships between the curvatures and the torsions of the Mannheim partner curves with respect to each other.
In this paper, using [E. Kasap, _ I. Aydemir, N. Kuruog ˘lu, Erratum to: ''Ruled surfaces with timelike rulings'' [Appl., some mistakes which are related to the classification maximal ruled surfaces with timelike rulings in the last section of [Applied Mathematics and Computation 147 (2004) 241–253 ] have been found and corrected then rewritten. A… (More)
In the present paper, we find a surface family possessing the natural lift of a given curve as a common asymptotic curve. We express necessary and sufficient conditions for the given curve such that its natural lift is an asymptotic curve on any member of the surface family. We present important results for ruled surfaces. Finally, we illustrate the method… (More)
abstract: In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for… (More)
A curve which is called geodesic on a surface M in Lorentz 3-space is a special curve that its acceleration is everywhere normal to M. In this paper, we analyzed the non-linear differential equation to determine the geodesic curves on ruled surfaces which is obtained by a strictly connected spacelike straight line moving with Frenet's frame along a timelike… (More)
In this article, a new type of ruled surfaces in a Lorentz 3-space R 3 1 is obtained by a strictly connected time-like oriented line moving with FrenetÕs frame along a space-like curve. These surfaces are classified into time-like and space-like surfaces. The well-known theorems due to Bonnet and Chasles in the 3-dimensional Euclidean space are proved for a… (More)