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

Abstract

In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to define a conformal invariant pair. For a 4-dimensional manifold, we compute this conformal invariant pair under some conditions and point out the way of computations in the general.

References in corpus (4)

• Gravity, Non-Commutative Geometry and the Wodzicki Residue
• Differential Forms and the Wodzicki Residue for Manifolds with Boundary
• Differential forms and the Wodzicki residue
• Connes' trace formula and Dirac realization of Maxwell and Yang-Mills action

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• Sub-signature Operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary
• Some Conformal Invariants from the Noncommutative Residue for Manifolds with Boundary
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• The J-twist D_J of the Dirac operator and the Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary
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• Dirac-Witten Operators and the Kastler-Kalau-Walze type theorem for manifolds with boundary