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Intrinsic wave mechanical behaviour in a Weyl-like geometry which conserves lengths

Einstein's lambda transformation and Weyl's gauge transformation are coupled to produce an asymmetric Weyl-like geometry. In the models of interest, lengths do not change under parallel transport. Automatic internal constraints of such geometries very closely resemble the equations of wave mechanics. Allowing an asymmetric metric tensor appears to add phenomena suggesting spin, although the equations are still scalar equations, not spinor ones. However, correspondence with Dirac theory exists for non-null, constant, uniform, electromagnetic fields in the limit that the symmetric part of the metric is Lorentzian.