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Real hypersurfaces in a complex projective space with pseudo- 𝔻 -parallel structure Jacobi operator

Hyunjin LeeJuan de Dios PérezYoung Jin Suh — 2010

Czechoslovak Mathematical Journal

We introduce the new notion of pseudo- 𝔻 -parallel real hypersurfaces in a complex projective space as real hypersurfaces satisfying a condition about the covariant derivative of the structure Jacobi operator in any direction of the maximal holomorphic distribution. This condition generalizes parallelness of the structure Jacobi operator. We classify this type of real hypersurfaces.

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II

Hyunjin LeeSeonhui KimYoung Jin Suh — 2014

Czechoslovak Mathematical Journal

Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces M of Type ( A ) in complex two plane Grassmannians G 2 ( m + 2 ) with a commuting condition between the shape operator A and the structure tensors φ and φ 1 for M in G 2 ( m + 2 ) . Motivated by this geometrical notion, in this paper we consider a new commuting condition in relation to the shape operator A and a new operator φ φ 1 induced by two structure tensors φ and φ 1 . That is, this commuting shape operator is given by φ φ 1 A = A φ φ 1 . Using this condition, we prove that...

Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition

Hyunjin LeeSeonhui KimYoung Jin Suh — 2012

Czechoslovak Mathematical Journal

In this paper, first we introduce a new notion of commuting condition that φ φ 1 A = A φ 1 φ between the shape operator A and the structure tensors φ and φ 1 for real hypersurfaces in G 2 ( m + 2 ) . Suprisingly, real hypersurfaces of type ( A ) , that is, a tube over a totally geodesic G 2 ( m + 1 ) in complex two plane Grassmannians G 2 ( m + 2 ) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G 2 ( m + 2 ) satisfying the commuting condition. Finally we get a characterization of Type ( A ) in terms of such commuting...

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