Ih thia paper, two binary operations on Lorentzian sphere in Rj and on Lorentzian cylinder in Rj are defined. Also, it has been shown that Lorentzian sphere in R| and Lorentzian cylinder in R® with the corresponding binary operation form Lie groups. A C°°-action on Lorentzian cylinder of arbitrary radius of Lorentzian cylinder of radius one is defined in R® and its •soıne properties are given. Finally, the action is expanded to Rj.