Reference : Conformal actions of higher-rank lattices on pseudo-Riemannian manifolds
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Physical, chemical, mathematical & earth Sciences : Mathematics
Conformal actions of higher-rank lattices on pseudo-Riemannian manifolds
Pecastaing, Vincent mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] Zimmer program ; Conformal geometry ; Pseudo-Riemannian geometry
[en] We investigate conformal actions of cocompact lattices in higher-rank simple Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a general bound on the real-rank of the lattice, which was already known for the action of the full Lie group ([33]). When the real-rank is maximal, we prove that the manifold is conformally flat. This indicates that a global conclusion similar to that of [1] and [17] in the case of a Lie group action might be obtained. We also give better estimates for actions of cocompact lattices in exceptional groups. Our work is strongly inspired by the recent breakthrough of Brown, Fisher and Hurtado on Zimmer’s conjecture [7].

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