Some Properties of Ruled Surfaces Under Homothety in E3

Abstract

It is clearly that, If f : E3 → E3 is a homothety and φ is a surface in three dimensional Euclidean space E3, f(φ) = φ̄ is also a surface in E3. In this paper, the surface φ has been taken a ruled surface, specially. It was shown that image surface f(φ) = φ̄ has been a ruled surface, too. Furthermore, It was investigated whether some properties related with ruled surfaces on φ have been invariant under the homothety f or not.