• Title/Summary/Keyword: pseudo anti-commuting ${\ast}$-Ricci tensor

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REAL HYPERSURFACES WITH ∗-RICCI TENSORS IN COMPLEX TWO-PLANE GRASSMANNIANS

  • Chen, Xiaomin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.975-992
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    • 2017
  • In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$, $m{\geq}3$, admitting commuting ${\ast}$-Ricci and pseudo anti-commuting ${\ast}$-Ricci tensor, respectively. As the applications, we prove that there do not exist ${\ast}$-Einstein metrics on Hopf hypersurfaces as well as ${\ast}$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.