Abstract

According to E. Study map in Minkowski space, we give in this present paper, a one-to-one correspondence between ”the curves on tangent bundles of Lorentzian (or de Sitter) unit sphere TS2 1 and hyperbolic unit sphere TH2” and ”the space-like or time-like ruled surface in E3 1”. In fact, we can consider each curve on TS2 1 or TH2 as a ruled surface in E3 1. Moreover, we study the relationships between the developability conditions of these corresponding ruled surfaces in E3 1 and their base and striction curves, and we show that if the curves on TS2 1 or TH2 are involute-evolute couples, then the corresponding ruled surfaces are developable.