A Kastler-Kalau-Walze Type Theorem About Dirac Operators For High-Dimensional Manifolds With Boundary

In this paper,we compute the lower dimensional volume Wres[?+D-3??+D-(2n-1)]on(2n+4)-dimensional spin manifolds with boundary,and we get associated Kastler-Kalau-Walze type theorem.As a corollary,we give a simple operator theoritic explaina-tion of the Einstein Hilbert gravitational action for(2n+4)-dimensional manifolds with boundary.