Browse > Article
http://dx.doi.org/10.4134/BKMS.b160414

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

Chen, Xiaomin (College of Science China University of Petroleum-Beijing)
Publication Information
Bulletin of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 975-992 More about this Journal
Abstract
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.
Keywords
commuting ${\ast}$-Ricci tensor; pseudo anti-commuting ${\ast}$-Ricci tensor; Hopf hypersurfaces; complex two-plane Grassmannians; ${\ast}$-Ricci soliton;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 J. Berndt and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math. 127 (1999), no. 1, 1-14.   DOI
2 J. Berndt and Y. J. Suh, Real hypersurfaces with isometric Reeb flows in complex two-plane Grassmannians, Monatsh. Math. 137 (2002), no. 2, 87-98.   DOI
3 T. Hamada, Real hypersurfaces of complex space forms in terms of Ricci *-tensor, Tokyo J. Math. 25 (2002), no. 2, 473-483.   DOI
4 R. Hamilton, The Ricci flow on surfaces, mathematics and general relativity, (Santa Cruz, CA, 1986), Contemp. Math. 71, pp. 237-262, Amer. Math. Soc., Providence, RI., 1988.
5 M. Kimura, Some real hypersurfaces of a complex projective space, Saitama Math. J. 5 (1987), 1-5.
6 I. Jeong and Y. J. Suh, Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians, J. Geom. Phys. 86 (2014), 258-272.   DOI
7 G. Kaimakamis, K. Panagiotidou, -Ricci solitons of real hypersurfaces in non-flat com- plex space forms, J. Geom. Phys. 86 (2014), 408-413.   DOI
8 M. Kimura, Real hypersurfaces and complex submanifolds in complex projective space, Trans. Amer. Math. Soc. 296 (1986), no. 1, 137-149.   DOI
9 H. Lee and Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians related to the Reeb vector, Bull. Korean Math. Soc. 47 (2010), no. 3, 551-561.   DOI
10 J. D. Perez and Y. J. Suh, Certain conditions on the Ricci tensor of real hypersurfaces in quaternionic projective space, Acta Math. Hungar. 91 (2001), no. 4, 343-356.   DOI
11 Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians, Monatsh. Math. 147 (2006), no. 4, 337-355.   DOI
12 Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor, J. Geom. Phys. 60 (2010), no. 11, 1792-1805.   DOI
13 Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor, Proc. Roy. Soc. Edinburgh 142A (2012), 1309-1324.