Tangent bundle of unit 2-sphere and slant ruled surfaces

Abstract

In this paper, an isomorphism between unit dual sphere, DS^2, and the subset of tangent bundle of unit 2-sphere, T\bar{M} is represented. According to E. Study mapping, a ruled surface in IR^3 corresponds to each curve on DS^2. Through this isomorphism, new forms of ruled surfaces called slant ruled surfaces in IR^3 were introduced. Moreover, conditions for these surfaces to be slant ruled surfaces were given. Finally, a unique \bar{q}, \bar{h} and \bar{a} slant ruled surfaces in IR^3 were corresponded to each striction curve of natural lift curve on T\bar{M}.