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

  • Suh, Young-Jin
  • 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>}.

Keywords

complex Grassmannians;real hypersurfaces;tubes;shape operator;Kahler structure;quaternionic Kahler structure.

References

  1. 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
  2. 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
  3. Rend. Sem. Mat. Univ. Politec Torino v.55 Riemannian geometry of complex two-plane Grassmannians J.Berndt
  4. 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
  5. Funct. Anal. Appl. v.2 Compact quaternion spaces D.V.Alekseevskii https://doi.org/10.1007/BF01075944
  6. 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
  7. 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
  8. 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
  9. Monatsh. Math v.127 Real hypersurfaces in complex two-plane Grassmannians J.Berndt;Y.J.Suh https://doi.org/10.1007/s006050050018
  10. J. Reine Angew. Math. v.419 Real hypersurfaces in quaternionic space forms J.Berndt
  11. Trans. Amer. Math. Soc. v.296 Real hypersurfaces and complex submanifolds in complex projective space M.Kimura https://doi.org/10.2307/2000565
  12. J. Geom. v.49 Real hypersurfaces of quaternionic projective space satisfying ∇$U_i$A=0 J.D.Perez https://doi.org/10.1007/BF01228059

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