Estimates for derivatives of the Green functions for the noncoercive differential operators on homogeneous manifolds of negative curvature. II.
On donne une caractérisation des groupes de Lie qui admettent une connexion invariante à gauche sans courbure ni torsion et dont la forme de connexion est à valeurs dans l’algèbre adjointe. On fait le lien entre cette question et le problème de platitude de certaines -structures invariantes à gauche sur les groupes de Lie.
These are expository notes from the 2008 Srní Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the Fubini-Griffiths-Harris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.
We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.