Tangent bundle of unit 2-sphere and slant ruled surfaces

Abstract

In this paper, an isomorphism between unit dual sphere, DS2, and the subset of tangent bundle of unit 2-sphere, T?M, is represented. According to E. Study mapping, a ruled surface in IR3 corresponds to each curve on DS2. Through this isomorphism, new forms of ruled surfaces called slant ruled surfaces in IR3 were introduced. Moreover, conditions for these surfaces to be slant ruled surfaces were given. Finally, a unique ?q?,?h? and ?? slant ruled surfaces in IR3 were corresponded to each striction curve of natural lift curve on T?M.