Suh, Young Jin Real hypersurfaces in complex two-plane Grassmannians with \(\xi \)-invariant Ricci tensor. (English) Zbl 1209.53046 J. Geom. Phys. 61, No. 4, 808-814 (2011). Summary: First we introduce the full expression of the Ricci tensor of a real hypersurface \(M\) in complex two-plane Grassmannians \(G_2(\mathbb C^{m+2})\) from the equation of Gauss. Next, we give a new characterization of real hypersurfaces of type \((A)\) in complex two-plane Grassamnnians with a vanishing Lie derivative of the Ricci tensor \(S\) in the direction of the Reeb vector field \(\xi \), that is, an \(\xi \)-invariant Ricci tensor. Cited in 1 ReviewCited in 11 Documents MSC: 53C40 Global submanifolds 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:real hypersurface; complex two-plane Grassmannian; commuting Ricci tensor; \(\xi \)-invariant Ricci tensor; Hopf hypersurface PDFBibTeX XMLCite \textit{Y. J. Suh}, J. Geom. Phys. 61, No. 4, 808--814 (2011; Zbl 1209.53046) Full Text: DOI References: [1] Kimura, M., Real hypersurfaces of a complex projective space, Bull. Aust. Math. Soc., 33, 383-387 (1986) · Zbl 0576.53016 [2] Kimura, M., Correction to “Some real hypersurfaces in complex projective space”, Saitama Math. J., 10, 33-34 (1992) · Zbl 0788.53052 [3] Ki, U.-H.; Suh, Y. J., On real hypersurfaces of a complex space form, Math. J. Okayama, 32, 205-221 (1990) · Zbl 0734.53040 [4] Pérez, J. D., On the Ricci tensor of a real hypersurfaces of quaternionic projective space, Int. J. Math. Math. Sci., 19, 193-197 (1996) · Zbl 0838.53023 [5] Berndt, J.; Suh, Y. J., Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 127, 1-14 (1999) · Zbl 0920.53016 [6] Berndt, J.; Suh, Y. J., Isometric flows on real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 137, 87-98 (2002) · Zbl 1015.53034 [7] Pérez, J. D.; Suh, Y. J., Real hypersurfaces of quaternionic projective space satisfying \(\nabla_{U_i} R = 0\), Differential Geom. Appl., 7, 211-217 (1997) · Zbl 0901.53011 [8] Suh, Y. J., Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator, Bull. Aust. Math. Soc., 68, 379-393 (2003) · Zbl 1058.53046 [9] Suh, Y. J., Real hypersurfaces in complex two-plane Grassmannians with vanishing Lie derivatives, Canad. Math. Bull., 49, 134-143 (2006) · Zbl 1100.53045 [10] Suh, Y. J., Real hypersurfaces of type \(B\) in complex two-plane Grassmannians, Monatsh. Math., 141, 337-355 (2006) · Zbl 1094.53050 [11] Berndt, J., Riemannian geometry of complex two-plane Grassmannians, Rend. Semin. Mat. Univ. Politec. Torino, 55, 19-83 (1997) · Zbl 0909.53038 [12] Alekseevskii, D. V., Compact quaternion spaces, Funct. Anal. Appl., 2, 106-114 (1966) [13] Suh, Y. J., Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor, J. Geom. Phys., 60-11, 1792-1805 (2010) · Zbl 1197.53070 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.