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REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR

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초록

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic QPn in complex two-plane Grassmannians G2(Cm+2), where m = 2n, with the Reeb vector ξ belonging to the distribution D, where D denotes a subdistribution in the tangent space TxM such that TxM = D⊕D┴ for any point x 2 M and D┴ = Span{ ξ1, ξ2, ξ3 }.

Abstract

In this paper we give a new characterization of real hypersurfaces of type B, that is, a tube over a totally geodesic QPn in complex two-plane Grassmannians G2(Cm+2), where m = 2n, with the Reeb vector ξ belonging to the distribution D, where D denotes a subdistribution in the tangent space TxM such that TxM = D⊕D┴ for any point x 2 M and D┴ = Span{ ξ1, ξ2, ξ3 }.

참고문헌 (11)

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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. T. E. Cecil, "Focal sets and real hypersurfaces in complex projective space", Trans. Amer. Math. Soc., 269(2), pp.481~499 (1982)
  6. 정임순, "REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE ξ-PARALLEL NORMAL JACOBI OPERATOR", 대한수학회지, 45(4), pp.1113~1133 (2008), 대한수학회
  7. M. Kimura, "Real hypersurfaces and complex submanifolds in complex projective space", Trans. Amer. Math. Soc., 296(1), pp.137~149 (1986)
  8. Y. J. Suh, "Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator", Bull. Austral. Math. Soc., 68(3), pp.379~393 (2003)
  9. Y. J. Suh, "Real hypersurfaces of type B in complex two-plane Grassmannians", Monatsh. Math., 147(4), pp.337~355 (2006)
  10. R. Takagi, "On homogeneous real hypersurfaces in a complex projective space", Osaka J. Math., 10, pp.495~506 (1973)
  11. K. Yano, "CR Submanifolds of Kaehlerian and Sasakian Manifolds" (1983), Birkhauser

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