Affine actions of higher rank lattices (Q1308684)

The paper is devoted to the actions of lattice subgroups of some higher rank semisimple Lie group \(G\) by diffeomorphisms of a compact, connected Riemannian manifold \(M\) which preserve the Levi-Civita connection of \(M\). Under the hypothesis that the dimension of \(M\) is sufficiently small, one obtains geometric informations for \(M\) and for the action from the algebraic properties of the representations of \(G\). As an application it is deduced a condition for an affine action on a vector bundle to preserve a compatible Riemannian metric.