Conformal vector fields and $\sigma_k$-scalar curvatures

Xingwang Xu and Jian Ye

Vol. 316 (2022), No. 2, 453–473

DOI: 10.2140/pjm.2022.316.453

Abstract

We discuss a new relationship between the conformal vector field and the ${\sigma }_k$-scalar curvature for general $k\ge 1$ on a closed manifold. The case $k=1$ is well known and has been widely used. Several applications of the identities derived for the general case are given.

Keywords

conformal vector field, $\sigma_k$-scalar curvature, maximum principle, Ricci curvature, locally conformally flat

Mathematical Subject Classification

Primary: 58J60

Secondary: 58J05

Milestones

Received: 9 March 2021

Revised: 28 September 2021

Accepted: 4 December 2021

Published: 6 April 2022