On preserved properties for slant ruled surfaces under homothety in $E^{3}$

Abstract

In mathematics, it is known that if $E^{3} \rightarrow E^{3}$ is a homothety and $N$ is a surface in $E^{3}$,  then $f(N)=\bar{N}$ is a surface in $E^{3}$.  In this study, especially, the surface $N$ is considered a slant ruled surface. Then, it is proved that the image surface $f(N)=\bar{N}$ is a slant ruled surface, too. Moreover, some significant properties are shown to be preserved under homothety in $E^{3}$.