Noncommutative Residue and Dirac operators for Manifolds with the Conformal Robertson-Walker metric

Abstract

In this paper, we prove a Kastler-Kalau-Walze type theorem for 4-dimensional and 6-dimensional spin manifolds with boundary associated with the conformal Robertson-Walker metric. And we give two kinds of operator theoretic explanations of the gravitational action for boundary in the case of 4-dimensional manifolds with flat boundary. In particular, for 6-dimensional spin manifolds with boundary with the conformal Robertson-Walker metric, we obtain the noncommutative residue of the composition of ${\pi }^{+}{D}^{-1}$ and ${\pi }^{+}{D}^{-3}$ is proportional to the Einstein-Hilbert action for manifolds with boundary.

arXiv admin note: substantial text overlap with arXiv:1211.6223, arXiv:1209.6211, arXiv:0907.3012, arXiv:math/0609058

References in corpus (1)

• Differential Forms and the Wodzicki Residue for Manifolds with Boundary