#### Vol. 316, No. 2, 2022

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Conformal vector fields and $\sigma_k$-scalar curvatures

### Xingwang Xu and Jian Ye

Vol. 316 (2022), No. 2, 453–473
##### 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
Primary: 58J60
Secondary: 58J05