The linear perturbation of the metric and the bimetric conformal invarints

TL;DR

This paper introduces a method to construct bimetric conformal invariants using linear metric perturbations and computes related invariants and variations, advancing understanding in conformal geometry.

Contribution

It presents a novel approach to constructing bimetric conformal invariants via linear perturbations and computes their variations, providing new insights in conformal geometry.

Findings

New bimetric conformal invariants on 4D Riemannian manifolds

First and second order variations of Connes conformal invariants

Explicit computation of metric perturbations of conformal invariants

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.