Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

REAL HYPERSURFACES OF TYPE A IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE NORMAL JACOBI OPERATOR

  • Jeong, Im-Soon (Department of Mathematics Kyungpook National University) ;
  • Suh, Young-Jin (Department of Mathematics Kyungpook National University) ;
  • Tripathi, Mukut Mani (Department of Mathematics and DST Centre for Interdisciplinary Mathematical Sciences Baranas Hindu University)
  • Received : 2010.12.14
  • Published : 2012.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we give a characterization of real hypersurfaces of type (A) in a complex two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ which is a tube over a totally geodesic $G_2(\mathbb{C}^{m+1})$ in $G_2(\mathbb{C}^{m+2})$, in terms of two commuting conditions related to the normal Jacobi operator and the shape operator.

Keywords

References

  1. D. V. Alekseevskii, Compact quaternion spaces, Func. Anal. Appl. 2 (1966), 106-114. https://doi.org/10.1007/BF01075944
  2. J. Berndt, Real hypersurfaces in quaternionic space forms, J. Reine Angew. Math. 419 (1991), 9-26.
  3. J. Berndt, Riemannian geometry of complex two-plane Grassmannians, Rend. Sem. Mat. Univ. Politec. Torino 55 (1997), no. 1, 19-83.
  4. J. Berndt and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math. 127 (1999), no. 1, 1-14. https://doi.org/10.1007/s006050050018
  5. J. Berndt and Y. J. Suh, Real hypersurfaces with isometric Reeb flows in complex two-plane Grassman- nians, Monatsh. Math. 137 (2002), no. 2, 87-98. https://doi.org/10.1007/s00605-001-0494-4
  6. I. Jeong and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with Lie -parallel normal Jacobi operator, J. Korean Math. Soc. 45 (2008), no. 4, 1113-1133. https://doi.org/10.4134/JKMS.2008.45.4.1113
  7. 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. https://doi.org/10.4134/BKMS.2010.47.3.551
  8. J. D. Perez, I. Jeong, and Y. J. Suh, Real hypersurfaces in complex two-plane Grass- mannians with commuting normal Jacobi operator, Acta Math. Hungar. 117 (2007), no. 3, 201-217. https://doi.org/10.1007/s10474-007-6091-9
  9. Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. Austral. Math. Soc. 67 (2003), no. 3, 493-502. https://doi.org/10.1017/S000497270003728X
  10. Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator II, J. Korean Math. Soc. 41 (2004), no. 3, 535-565. https://doi.org/10.4134/JKMS.2004.41.3.535
  11. Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with vanishing Lie derivatives, Canad. Math. Bull. 49 (2006), no. 1, 134-143. https://doi.org/10.4153/CMB-2006-014-8
  12. Y. J. Suh, Real hypersurfaces of type B in complex two-plane Grassmannians, Monatsh. Math. 147 (2006), no. 4, 337-355. https://doi.org/10.1007/s00605-005-0329-9