Model form for exact b-metrics

Any manifold with boundary can be equipped with a b-metric which takes the form dx(2)/x(2) + h(x; y; dx; dy) with respect to some product decompositio n near the boundary, and h positive definite on restriction to the tangent space of the boundary. Here we show the existence of a product decompositio n such that h is independent of dx modulo terms vanishing to infinite order at the boundary. The uniqueness of this decomposition is also examined.