Some Properties of Ruled Surfaces under Homothety in $E^3$

Abstract

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