Similar Ruled Surfaces with Variable Transformations in Minkowski 3-Space E_1^3

Similar Ruled Surfaces with Variable Transformations in Minkowski 3-Space

M. Önder

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Abstract

In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space E3 1 . We obtain some properties of these special surfaces in E3 1 and show that developable ruled surfaces in E3 1 form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curves with variable transformation. Moreover, we obtain that cylindrical surfaces and conoids form two families of similar ruled surfaces in E31 .

Keywords

Timelike and spacelike ruled surfaces; Frenet frame; similar curve.