Twisted Dirac Operators and the Noncommutative Residue for Manifolds with Boundary

In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature operators on 4-dimensional manifolds with (resp. without) boundary.Comment: arXiv admin note: text overlap with arXiv:1303.371

A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with Boundary

The Kastler-Kalau-Walze theorem, announced by Alain Connes, shows that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. In this paper, we prove a Kastler-Kalau-Walze type theorem for 5-dimensional manifolds with boundary.Comment: arXiv admin note: text overlap with arXiv:1303.3713, arXiv:1404.233