New time-changes of unipotent flows on quotients of Lorentz groups

<p style='text-indent:20px;'>We study the cocompact lattices <inline-formula><tex-math id="M1">\begin{document}$ \Gamma\subset SO(n, 1) $\end{document}</tex-math></inline-formula> so that Laplace–Beltrami operator id="M2">\begin{document}$ \Delta on id="M3">\begin{document}$ SO(n)\backslash 1)/\Gamma has eigenvalues in id="M4">\begin{document}$ (0, \frac{1}{4}) $\end{document}</tex-math></inline-formula>, and then show there exist time-changes of unipotent flows id="M5">\begin{document}$ are not measurably conjugate to unperturbed ones. A main ingredient proof is a stronger version branching complementary series. Combining it with refinement works Ratner Flaminio–Forni adequate for our purpose.</p>