Conformally Einstein Lorentzian Lie groups with Heisenberg symmetry
Esteban Calvi\~no-Louzao, Eduardo Garcia-Rio, Ixchel, Gutierrez-Rodriguez, Ramon Vazquez-Lorenzo
TL;DR
This paper classifies conformally Einstein Lorentzian Lie groups with Heisenberg symmetry, providing new solutions in conformal gravity by analyzing semi-direct extensions of the Heisenberg group.
Contribution
It offers a complete classification of conformally Einstein Lorentzian semi-direct extensions of the Heisenberg group, including Bach-flat metrics.
Findings
All conformally Einstein Lorentzian semi-direct extensions of the Heisenberg group are described.
Bach-flat left-invariant Lorentzian metrics on these groups are classified.
New background solutions in conformal gravity are identified.
Abstract
We describe all Lorentzian semi-direct extensions of the Heisenberg group which are conformally Einstein. As a by side result, Bach-flat left-invariant Lorentzian metrics on semi-direct extensions of the Heisenberg group are classified, thus providing new background solutions in conformal gravity.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Geometry Research · Geometric Analysis and Curvature Flows · Geometry and complex manifolds