On non-positive Weyl connection on Lie groups

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.