Journal of the
Korean Mathematical Society JKMS

In this paper, we introduce the notion of stress-energy tensor $Q$ of the traceless Ricci tensor for Riemannian manifolds $(M^n, g)$, and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when $(M, g)$ satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

Keywords: Conservative law, harmonic curvature, stress-energy tensor, traceless Ricci tensor, vacuum static equation

MSC numbers: Primary 53C25; Secondary 58E11

Supported by: This paper was supported by Myongji University Research Year Grant (from 2022. 03 to 2023. 02). This paper was supported by Myongji University Research Year Grant (from 2022. 03 to 2023. 02).