Geometry Seminar: C. Böhm (University of Münster)

Geometry Seminar (Geometric Analysis)

Speaker: Christoph Böhm (University of Münster)

Title: The cohomogeneity one Einstein ODE

Abstract: For a Riemannian manifold $(M^n,g)$ the Einstein equation $ricg(g)=\lambda \cdot g$ is (weakly) elliptic. Assuming symmetry this second order PDE simplifies: If the Riemannian manifold is homogeneous the Einstein equation turns into an algebraic equation. If the Riemannian manifold is of cohomogeneity one, the Einstein equation becomes a highly non-linear dynamical system, the cohomogeneity one Einstein ODE. In this talk will present general structure results for the cohomogeneity one Einstein ODE both for positive and non-positive Einstein constant $\lambda$.