The linear perturbation of the metric and the bimetric conformal invarints

Abstract

In this paper, we give a method to construct bimetric conformal invarints by the linear metric perturbations and the conformal invarints. And we compute the metric perturbations of the Connes conformal invarints and the conformal Laplacian. As corollaries, some new bimetric conformal invarints on 4-dimensional Riemannian manifolds without boundary are obtained and we get the first order and second order variations of the Connes conformal invarints.