The Kastler-kalau-walze Type Theorem About Witten Deformation For Manifolds With Boundary

In this thesis,we compute the lower dimensional volume Vol₆^（1,3）for 6-dimensional spin manifolds with boundary and the gravity on boundary is de-rived by the noncommutative residue associated with Witten deformation.We also give a theoritic explaination of the gravitational action for 6 dimensional manifolds with boundary by the noncommutative residue associated with Witten deformation.