Negative Ricci curvature on complex simple Lie groups
type: Item
instance of: scholarly article
title: Negative Ricci curvature on complex simple Lie groups
zbMATH Open document ID: 0549.53049
author: Isabel Dotti de Miatello
author: Maria Luiza Leite
author: R. J. Miatello
published in: Geometriae Dedicata
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 57S15
zbMATH DE Number: 3876136
zbMATH Keywords: simple Lie groups
zbMATH Keywords: left invariant metrics
zbMATH Keywords: Ricci curvature
zbMATH Keywords: unimodular Lie group
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3876136