Rigidity of joinings for time changes of unipotent flows on quotients of Lorentz groups

Abstract Let $u_{X}^{t}$ be a unipotent flow on $X=\mathrm {SO}(n,1)/\Gamma $ , $u_{Y}^{t}$ $Y=G/\Gamma ^{\prime }$ . $\tilde {u}_{X}^{t}$ {u}_{Y}^{t}$ time changes of respectively. We show the disjointness (in sense Furstenberg) between and (or ) in certain situations. Our method refines works Ratner’s shearing argument. The also extends recent work Dong, Kanigowski, Wei [Rigidity joinings for some measure preserving systems. Ergod. Th. & Dynam. Sys. 42 (2022), 665–690].