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In this paper, for an even dimensional compact manifold with boundary whichhas the non-product metric near the boundary, we use the noncommutative residueto define a conformal invariant pair. For a 4-dimensional manifold, we computethis conformal invariant pair under some conditions and point out the way ofcomputations in the general

Differential Forms and the Noncommutative Residue for Manifolds with Boundary in the Non-product Case