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 σk-scalar curvature for general k 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
Authors
Xingwang Xu
Department of Mathematics
Nanjing University
Nanjing
China
Jian Ye
Department of Mathematics
Nanjing University
Nanjing
China