Non-Einstein relative Yamabe metrics

TL;DR

This paper establishes a sufficient condition for positive scalar curvature metrics on manifolds with boundary to be relative Yamabe metrics and provides examples of non-Einstein such metrics.

Contribution

It introduces a new sufficient condition for relative Yamabe metrics and presents the first known examples of non-Einstein positive scalar curvature relative Yamabe metrics.

Findings

Identified a sufficient condition for relative Yamabe metrics with positive scalar curvature.

Constructed examples of non-Einstein relative Yamabe metrics.

Extended the understanding of the structure of Yamabe metrics on manifolds with boundary.

Abstract

In this paper, we give a sufficient condition for a positive constant scalar curvature metric on a manifold with boundary to be a relative Yamabe metric, which is a natural relative version of the classical Yamabe metric. We also give examples of non-Einstein relative Yamabe metrics with positive scalar curvature.