Negative Ricci metrics on Lie groups with compact Levi factor

WILL, CYNTHIA

La Falda

Workshop; VI Workshop on Differential Geometry; 2016

The question of when a differentiable manifold admits a Riemannian metric with a particular sign of the curvature is a very natural one. For homogeneous Riemannian manifolds, the case of sectional curvature is quite restrictive and well understood. Concerning negative Ricci curvature, although a great progress has been made lately, specially in the solvable case, the general case seems to be far from being completely understood. In this talk, we will begin by introducing the known results on negative Ricci curvature in the homogeneous case, and then we will show some unexpected examples of Lie groups with compact Levi factor that admits a metric with negative Ricci curvature.