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In this article, we consider a real hypersurface of complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2}),m\geq3$, admitting commuting $*$-Ricci and pseudo anti-commuting $*$-Ricci tensor, respectively. As the applications, we prove that there do not exist $*$-Einstein metrics on Hopf hypersurfaces as well as $*$-Ricci solitons whose potential vector field is the Reeb vector field on any real hypersurfaces.
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참고문헌 (13)
참고문헌 신청
G. Kaimakamis / 2014 / *-Ricci solitons of real hypersurfaces in non-flat com-plex space forms / J. Geom. Phys 86 : 408 ~ 413
I. Jeong / 2014 / Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians / J. Geom. Phys 86 : 258 ~ 272
J. Berndt / 1999 / Real hypersurfaces in complex two-plane Grassmannians / Monatsh. Math 127 (1) : 1 ~ 14
J. Berndt / 2002 / Real hypersurfaces with isometric Reeb flows in complex two-plane Grassman-nians / Monatsh. Math 137 (2) : 87 ~ 98
J. D. P´erez / 2001 / Certain conditions on the Ricci tensor of real hypersurfaces in quaternionic projective space / Acta Math. Hungar 91 (4) : 343 ~ 356
I. Jeong / 2014 / Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians / J. Geom. Phys 86 : 258 ~ 272
J. Berndt / 1999 / Real hypersurfaces in complex two-plane Grassmannians / Monatsh. Math 127 (1) : 1 ~ 14
J. Berndt / 2002 / Real hypersurfaces with isometric Reeb flows in complex two-plane Grassman-nians / Monatsh. Math 137 (2) : 87 ~ 98
J. D. P´erez / 2001 / Certain conditions on the Ricci tensor of real hypersurfaces in quaternionic projective space / Acta Math. Hungar 91 (4) : 343 ~ 356
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