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Using the metric tensor galphabeta, the author derives the scattering parameters appearing in the field equations of the uniform theory of diffraction (UTD). The method presented allows us to derive these field parameters in terms of tensors whose general form can be applied to high-frequency electromagnetic scattering problems or more specifically to the analysis of conformal arrays. All the parameters in the field solutions are related to the array manifold properties that are derived via the use of the metric tensor are shown. The expressions for the Frenet-field tensors and the generalised Fock parameter and the shortest path propagated by the fields along the array manifold using the metric tensor in the calculus of variations are determined. The method enables UTD mutual coupling calculations to be performed for various phased array manifolds.