Solvable Lie groups of negative Ricci curvature
Abstract
We consider the question of whether a given solvable Lie group admits a leftinvariant metric of strictly negative Ricci curvature. We give necessary and sufficient conditions of the existence of such a metric for the Lie groups the nilradical of whose Lie algebra is either abelian or Heisenberg or standard filiform, and discuss some open questions.
 Publication:

arXiv eprints
 Pub Date:
 December 2013
 arXiv:
 arXiv:1312.6803
 Bibcode:
 2013arXiv1312.6803N
 Keywords:

 Mathematics  Differential Geometry;
 53C30;
 22E25
 EPrint:
 18 pages