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)
the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We investigate minimal surfaces passing a given curve in R 3. Using the Frenet frame of a given curve and isothermal parameter, we derive the necessary and sufficient condition for… (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)