Ruled Surfaces and Tangent Bundle of Unit 2-Sphere of Natural Lift Curves

Abstract

This article deals with the isomorphism between unit dual sphere, 𝐷𝑆2, and the subset of thetangent bundle of unit 2-sphere, 𝑇𝑀 ̅ . According to E. Study mapping, a ruled surfacein ℝ3corresponds to each curve on 𝐷𝑆2. Through this correspondence, a unique ruled surface inℝ3is corresponded to natural lift curve on 𝑇𝑀 ̅. Then striction curve, shape operator, meancurvature and Gaussian curvature of these ruled surfaces obtained by the natural lift curves arecalculated. Developabilitiy condition of these ruled surfaces is given. Finally, we give an exampleto support the main results.