The affine group of a compact Riemannian manifold (Q1366527)

Let \(M\) be a compact Riemannian manifold. The isometry group \(\text{Isom}(M)\) of \(M\) becomes naturally a compact Lie group. The author investigates the problem whether there is a geometric structure which is weaker than the metric structure for which the group of transformations of \(M\) preserving this structure becomes a noncompact Lie group. In fact, the author considers the connection of Levi-Civita induced by the Riemannian metric and shows that if there is a noncompact group action preserving this connection, then the manifold is restricted to fairly special types of compact manifolds.