Reference : Conformal actions of higher-rank lattices on pseudo-Riemannian manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/39064
Conformal actions of higher-rank lattices on pseudo-Riemannian manifolds
English
Pecastaing, Vincent mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2020
Geometric and Functional Analysis
Birkhauser Verlag
30
955-987
Yes (verified by ORBilu)
International
1016-443X
1420-8970
Switzerland
[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].
Researchers
http://hdl.handle.net/10993/39064

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