Abstract
In this article, we consider a real hypersurface of complex two-plane Grassmannians <TEX>$G_2({\mathbb{C}}^{m+2})$</TEX>, <TEX>$m{\geq}3$</TEX>, admitting commuting <TEX>${\ast}$</TEX>-Ricci and pseudo anti-commuting <TEX>${\ast}$</TEX>-Ricci tensor, respectively. As the applications, we prove that there do not exist <TEX>${\ast}$</TEX>-Einstein metrics on Hopf hypersurfaces as well as <TEX>${\ast}$</TEX>-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.
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