In this paper, for lower dimensional spin manifolds with boundary, we prove the Kastler–Kalau–Walze type theorems for the Dirac operator associated with conformal Robertson–Walker metric. We find the gravitational action for manifolds with boundaries, which is associated with asymmetric operators, and yields the boundary term.

中文翻译：

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重力，Robertson-Walker度量和Wodzicki残差

在本文中，对于具有边界的低维自旋流形，我们证明了Dirac算子的Kastler-Kalau-Walze型定理与保形Robertson-Walker度量相关。我们发现了带边界流形的引力作用，它与不对称算子有关，并产生边界项。