Negative Ricci curvature on complex simple Lie groups (Q799952)

In this article we characterize (with a finite number of exceptions) the complex simple and split real simple Lie groups admitting left invariant metrics with negative Ricci curvature. As a consequence we obtain new examples of compact Riemannian manifolds with \(Ric<0\), which do not admit metrics with \(K\leq 0\), and where a compact, non commutative Lie group acts freely. We also prove that a unimodular Lie group admitting a left invariant metric with \(Ric<0\) must be semisimple and non compact.