A class of variational functionals in conformal geometry

TL;DR

This paper introduces a new class of variational functionals in conformal geometry, generalizing known functionals related to the Schouten tensor in locally conformal flat manifolds.

Contribution

It derives a broad class of variational functionals that extend existing functionals associated with the Schouten tensor in conformal geometry.

Findings

Functional coincides with known integrals in locally conformal flat cases

Provides a unified framework for variational functionals in conformal geometry

Potential applications in geometric analysis and conformal invariants

Abstract

We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the integration over the manifold of the k-symmetric function of the Schouten tensor of the metric on the manifold.