DOI QR코드

DOI QR Code

REAL HYPERSUREAACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH PARALLEL SHAPE OPERATOR II

  • Suh, Young-Jin (Department of Mathematics Kyungpook National University)
  • Published : 2004.05.01

Abstract

In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2$( $C^{m+2}$) and prove that there do not exist such kinds of real hypersurfaces in $G_2$( $C^{m+2}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span {ξ$_1$, ξ$_2$, ξ$_3$}.X>}.

References

  1. Funct. Anal. Appl. v.2 Compact quaternion spaces D.V.Alekseevskii https://doi.org/10.1007/BF01075944
  2. J. Reine Angew. Math. v.419 Real hypersurfaces in quaternionic space forms J.Berndt
  3. Rend. Sem. Mat. Univ. Politec Torino v.55 Riemannian geometry of complex two-plane Grassmannians J.Berndt
  4. Monatsh. Math v.127 Real hypersurfaces in complex two-plane Grassmannians J.Berndt;Y.J.Suh https://doi.org/10.1007/s006050050018
  5. Monatsh. Math. v.137 Isometric flows on real hypersurfaces in complex two-plane Grassmannians J.Berndt;Y.J.Suh https://doi.org/10.1007/s00605-001-0494-4
  6. Trans. Amer. Math. Soc. v.269 Focal sets and real hypersurfaces in complex projective space T.E.Cecil;P.J.Ryan https://doi.org/10.2307/1998460
  7. Trans. Amer. Math. Soc. v.296 Real hypersurfaces and complex submanifolds in complex projective space M.Kimura https://doi.org/10.2307/2000565
  8. Tsukuba J. Math. v.15 On real hypersurfaces of a compoex projective space Ⅱ M.Kimura;S.Maeda https://doi.org/10.21099/tkbjm/1496161675
  9. J. Geom. v.49 Real hypersurfaces of quaternionic projective space satisfying ∇$U_i$A=0 J.D.Perez https://doi.org/10.1007/BF01228059
  10. Diff. Geom. Appl. v.7 Real hypersurfaces of quaternionic projective space satisfying ∇$U_i$R=0 J.D.Perez;Y.J.Suh https://doi.org/10.1016/S0926-2245(97)00003-X
  11. Bull. Austral. Math. Soc. v.67 Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator Y.J.Suh https://doi.org/10.1017/S000497270003728X
  12. Bull. Austral. Math. Soc. v.68 Real hypersurfaces in comples two-plane Grassmannians with commuting shpae operator Y.J.Suh https://doi.org/10.1017/S0004972700037795

Cited by

  1. Levi-Civita and generalized Tanaka–Webster covariant derivatives for real hypersurfaces in complex two-plane Grassmannians vol.194, pp.3, 2015, https://doi.org/10.1007/s10231-014-0405-7
  2. REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS SOME OF WHOSE JACOBI OPERATORS ARE ξ-INVARIANT vol.23, pp.03, 2012, https://doi.org/10.1142/S0129167X1100746X
  3. Real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator is of Codazzi type vol.125, pp.1-2, 2009, https://doi.org/10.1007/s10474-009-8245-4
  4. Real hypersurfaces in complex two-plane grassmannians with parallel structure Jacobi operator vol.122, pp.1-2, 2009, https://doi.org/10.1007/s10474-008-8004-y
  5. REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH 𝔇⊥-PARALLEL STRUCTURE JACOBI OPERATOR vol.22, pp.05, 2011, https://doi.org/10.1142/S0129167X11006957
  6. Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians vol.31, pp.1, 2015, https://doi.org/10.1007/s10114-015-1765-7
  7. Real hypersurfaces in complex two-plane Grassmannians with commuting normal Jacobi operator vol.117, pp.3, 2007, https://doi.org/10.1007/s10474-007-6091-9
  8. Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster Reeb parallel shape operator vol.171, pp.3-4, 2013, https://doi.org/10.1007/s00605-013-0475-4
  9. Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Shape Operator vol.38, pp.2, 2015, https://doi.org/10.1007/s40840-014-0039-3
  10. REAL HYPERSURFACES OF TYPE A IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE NORMAL JACOBI OPERATOR vol.49, pp.2, 2012, https://doi.org/10.4134/BKMS.2012.49.2.423
  11. Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians vol.177, pp.4, 2015, https://doi.org/10.1007/s00605-015-0778-8
  12. Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator vol.51, pp.4, 2011, https://doi.org/10.5666/KMJ.2011.51.4.395
  13. Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor vol.64, 2013, https://doi.org/10.1016/j.geomphys.2012.10.005
  14. Real Hypersurfaces in Complex Two-plane Grassmannians with $${\mathfrak{D}^{\bot}}$$ -Parallel Shape Operator vol.64, pp.3-4, 2013, https://doi.org/10.1007/s00025-013-0317-7
  15. REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH GENERALIZED TANAKA–WEBSTER 𝔇⊥-PARALLEL SHAPE OPERATOR vol.09, pp.04, 2012, https://doi.org/10.1142/S0219887812500326
  16. HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR vol.48, pp.2, 2011, https://doi.org/10.4134/BKMS.2011.48.2.427
  17. Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type vol.01, pp.03, 2011, https://doi.org/10.4236/apm.2011.13015