Determine whether vanishing Galilean Weyl curvature implies conformal flatness

Determine whether the vanishing of the Galilean Weyl tensor implies conformal flatness of the Galilean structure.

Background

The paper establishes conformal invariance of the proposed Galilean Weyl tensor but does not characterize the geometric consequences of its vanishing. In particular, it leaves unresolved whether zero Galilean Weyl curvature is sufficient to guarantee conformal flatness, as happens in the relevant relativistic setting under appropriate dimensional assumptions.