Nonminimal operators and non-commutative residue

Abstract

In this paper, we get the Kastler-Kalau-Walze type theorem associated to nonminimal operators by heat equation asymptotics on compact manifolds without boundary. We compute the lower-dimensional volume associated to nonminimal operators for five-dimensional compact manifolds with boundary and we also compute lower-dimensional volume associated to the De-Rham Hodge operators for six-dimensional compact manifolds with boundary.