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 \(E^{3}\).