$\eta $-Einstein contact metric manifolds with purely transversal Bach tensor
Volume 126 / 2021
Annales Polonici Mathematici 126 (2021), 241-250
MSC: Primary 53C25; Secondary 53D10.
DOI: 10.4064/ap201007-18-2
Published online: 17 May 2021
Abstract
We prove that every ($2n+1$)-dimensional $\eta $-Einstein contact metric manifold (i.e., the Ricci tensor $S$ satisfies $S = \alpha g + \beta \eta \otimes \eta $ for some smooth functions $\alpha , \beta $) with purely transversal Bach tensor is Einstein.
