Bull. Korean Math. Soc. 2022; 59(5): 1167-1176
Online first article June 23, 2022 Printed September 30, 2022
https://doi.org/10.4134/BKMS.b210671
Copyright © The Korean Mathematical Society.
Seungsu Hwang, Gabjin Yun
Chung-Ang University; Myong Ji University
In this paper, we study Einstein-type manifolds generalizing static spaces and $V$-static spaces. We prove that if an Einstein-type manifold has non-positive complete divergence of its Weyl tensor and non-negative complete divergence of Bach tensor, then $M$ has harmonic Weyl curvature. Also similar results on an Einstein-type manifold with complete divergence of Riemann tensor are proved.
Keywords: Einstein-type manifold, complete divergence, harmonic Weyl curvature
MSC numbers: Primary 53C25; Secondary 53C20
Supported by: The first author was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education(NRF-2018R1D1A1B05042186), and the second author by the Ministry of Education(NRF-2019R1A2C1004948).
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