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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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