Induction of geometric actions (Q5956147)

Let \(N\) be a closed normal subgroup of a Lie group \(G\), and let \(M\) be a manifold on which \(N\) acts smoothly. The author considers the process of induction (or suspension), i.e., the smooth action of \(G\) on the manifold \(G \times_N M:=(G\times M)/N\), and describes some situations in which a geometric structure is preserved. This implies, in combination whith some known rigidity results, certain rigidity statements concerning the full diffeomorphism group of a manifold, and also provides many examples of actions on Lorentz manifolds. By using this, he gets the full list of connected simply connected Lie groups admitting a locally faithful, orbit non proper action by isometries of a connected Lorentz manifold. Other complementary examples and related results are also discussed.