On non-positive Weyl connection on Lie groups

Tomasz Dudek; Aleksy Tralle

On non-positive Weyl connection on Lie groups

Differential Geometry 2026-07-19 v1

Authors: Tomasz Dudek , Aleksy Tralle

Abstract

The paper contributes to the problem of finding non-positive invariant Weyl connections on Lie groups. The main result is that in the case of completely solvable 3-dimensional Lie groups only the group SOL admits such connections, confirming the conjecture of Wojtkowski. We conjecture that our method can be extended to the general case of completely solvable Lie groups.

Keywords

Weyl connections Lie groups non-positive curvature completely solvable SOL group

Cite

@article{arxiv.2607.17210,
  title  = {On non-positive Weyl connection on Lie groups},
  author = {Tomasz Dudek and Aleksy Tralle},
  journal= {arXiv preprint arXiv:2607.17210},
  year   = {2026}
}

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26 pages