Ricci Semi-symmetric Hypersurfaces in Complex Two-Plane Grassmannians
Tóm tắt
In this paper, we considered Ricci semi-symmetric real hypersurface in complex two-plane Grassmannians. Then we prove the non-existence of Ricci semi-symmetric Hopf hypersurfaces in complex two-plane Grassmannians by using the method of simultaneous diagonalization for pairwise commutative matrices.
Tài liệu tham khảo
Alekseevskii, D.V.: Compact quaternion spaces. Funct. Anal. Appl. 2, 106–114 (1966)
Berndt, J., Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians. Mon. Math. 127, 1–14 (1999)
Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambrige University Press, Cambrige (1985)
Jeong, I., Machado, C.J.G., Pérez, J.D., Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with \({\mathfrak{D}}^{\bot }\)-parallel structure Jacobi operator. Int. J. Math. 22(5), 655–673 (2011)
Jun, J.B., De, U.C., Pathak, G.: On Kenmotsu manifolds. J. Korean Math. Soc. 42(3), 435–445 (2005)
Lee, H., Choi, Y.S., Woo, C.: Hopf hypersurfaces in complex two-plane Grassmannians with Reeb parallel shape operator. Bull. Malays. Math. Soc. 38, 617–634 (2015)
Lee, H., Suh, Y.J.: Real hypersurfaces of Type B in complex two-plane Grassmannians related to the Reeb vector. Bull. Korean Math. Soc. 47(3), 551–561 (2010)
Lee, H., Suh, Y.J., Woo, C.: Real hypersurfaces with commuting Jacobi operators in complex two-plane Grassmannians. Houst. J. Math. 40(3), 751–766 (2014)
Loo, T.-H.: Semi-parallel real hypersurfaces in complex two-plane Grassmannians. Differ. Geom. Appl. 34, 87–102 (2014)
Panagiotidou, K., Tripathi, M.M.: Semi-parallelism of normal Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians. Mon. Math. 172(2), 167–178 (2013)
Pak, E., Suh, Y.J., Woo, C.: Real hypersurfaces in complex two-plane Grassmannians with commuting restricted Jacobi operators. Houst. J. Math. 41(3), 767–783 (2015)
Pérez, J.D., Suh, Y.J.: The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians. J. Korean Math. Soc. 44, 211–235 (2007)
Pérez, J.D., Suh, Y.J., Woo, C.: Real hypersurfaces in complex two-plane Grassmannians with GTW Harmonic curvature. Can. Math. Bull. 58(4), 835–845 (2015)
Pérez, J.D., Suh, Y.J., Woo, C.: Real hypersurfaces in complex two-plane Grassmannians whose shape operator is recurrent for the generalized Tanaka-Webster connection. Turk. J. Math. 39(3), 313–321 (2015)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor. J. Geom. Phys. 60, 1792–1805 (2010)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor. Proc. R. Soc. Edinb. A. 142, 1309–1324 (2012)
Suh, Y.J.: Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor. J. Geom. Phys. 64, 1–11 (2013)
Suh, Y.J., Hwang, D.H., Woo, C.: Real hypersurfaces in complex two-plane Grassmannians with recurrent Ricci tensor. Int. J. Geom. Methods Mod. Phys. 12(9), 1550086 (2015)