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Commuting structure Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians

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In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians G_(2)(C^(m+2)) satisfying the condition that the structure Jacobi operator R_(ξ) commutes with the 3-structure tensors Φ_(i),i=1,2,3.

Abstract

In this paper we give a non-existence theorem for Hopf real hypersurfaces in complex two-plane Grassmannians G_(2)(C^(m+2)) satisfying the condition that the structure Jacobi operator R_(ξ) commutes with the 3-structure tensors Φ_(i),i=1,2,3.

참고문헌 (9)

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  4. J. Berndt, "Real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians", Monatsh. Math, 137(2), pp.87~98 (2002)
  5. U-Hang KiJuan De Dios P'erezFlorentino G. SantosY, "Real hypersurfaces in complex spaceforms with xi-parallel Ricci tensor and structure Jacobioperator", 대한수학회지, 44(2), pp.307~326 (2007), 대한수학회
  6. M. Kimura, "Real hypersurfaces and complex submanifolds in complex projective space", Trans. Amer. Math. Soc, 296(1), pp.137~149 (1986)
  7. J. D. P´erez, "Real hypersurfaces of quaternionic projective space satisfying rUiR = 0", Differential Geom. Appl, 7(3), pp.211~217 (1997)
  8. J. D. P´erez, "Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie »-parallel", Differential Geom. Appl., 22(2), pp.181~188 (2005)
  9. J. D. P´erez, "Real hypersurfaces in complex projective space whose structure Jacobi operator is D-parallel", Bull. Belg. Math. Soc. Simon Stevin, 13(3), pp.459~469 (2006)

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