Real hypersurfaces with *-Ricci tensors in complex two-plane Grassmannians
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (13)
- J. Berndt, "Real hypersurfaces in complex two-plane Grassmannians", Monatsh. Math, 127(1), pp.1~14 (1999)
- J. Berndt, "Real hypersurfaces with isometric Reeb flows in complex two-plane Grassman-nians", Monatsh. Math, 137(2), pp.87~98 (2002)
- T. Hamada, "Real hypersurfaces of complex space forms in terms of Ricci *-tensor", Tokyo J. Math, 25(2), pp.473~483 (2002)
- R. Hamilton, "The Ricci flow on surfaces, mathematics and general relativity", pp.237~262 (1988), Amer. Math. Soc.
- I. Jeong, "Pseudo anti-commuting and Ricci soliton real hypersurfaces in complex two-plane Grassmannians", J. Geom. Phys, 86, pp.258~272 (2014)
- G. Kaimakamis, "*-Ricci solitons of real hypersurfaces in non-flat com-plex space forms", J. Geom. Phys, 86, pp.408~413 (2014)
- M. Kimura, "Real hypersurfaces and complex submanifolds in complex projective space", Trans. Amer. Math. Soc, 296(1), pp.137~149 (1986)
- M. Kimura, "Some real hypersurfaces of a complex projective space", Saitama Math. J, 5, pp.1~5 (1987)
- 이현진, "REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR", 대한수학회보, 47(3), pp.551~561 (2010), 대한수학회
- J. D. P´erez, "Certain conditions on the Ricci tensor of real hypersurfaces in quaternionic projective space", Acta Math. Hungar, 91(4), pp.343~356 (2001)
- Y. J. Suh, "Real hypersurfaces of type B in complex two-plane Grassmannians", Monatsh. Math, 147(4), pp.337~355 (2006)
- Y. J. Suh, "Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor", J. Geom. Phys, 60(11), pp.1792~1805 (2010)
- Y. J. Suh, "Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor", Proc. Roy. Soc. Edinburgh, 142A, pp.1309~1324 (2012)