Solvable Lie groups of negative Ricci curvature
Abstract
We consider the question of whether a given solvable Lie group admits a left-invariant 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:
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arXiv e-prints
- Pub Date:
- December 2013
- arXiv:
- arXiv:1312.6803
- Bibcode:
- 2013arXiv1312.6803N
- Keywords:
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- Mathematics - Differential Geometry;
- 53C30;
- 22E25
- E-Print:
- 18 pages