Displaying similar documents to “A characterization of totally η -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form”

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

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2014)

Czechoslovak Mathematical Journal

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Lee, Kim and Suh (2012) gave a characterization for real hypersurfaces M of Type ( A ) in complex two plane Grassmannians G 2 ( ℂ m + 2 ) with a commuting condition between the shape operator A and the structure tensors φ and φ 1 for M in G 2 ( ℂ 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...

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

Hyunjin Lee, Seonhui Kim, Young Jin Suh (2012)

Czechoslovak Mathematical Journal

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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 ( ℂ m + 2 ) . Suprisingly, real hypersurfaces of type ( A ) , that is, a tube over a totally geodesic G 2 ( ℂ m + 1 ) in complex two plane Grassmannians G 2 ( ℂ m + 2 ) satisfy this commuting condition. Next we consider a complete classification of Hopf hypersurfaces in G 2 ( ℂ m + 2 ) satisfying the commuting condition. Finally we get a characterization of Type ( A ) in terms of such...

Real hypersurfaces in complex space forms concerned with the local symmetry

Seon Mi Lyu, Juan de Dios Pérez, Young Jin Suh (2007)

Czechoslovak Mathematical Journal

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This paper consists of two parts. In the first, we find some geometric conditions derived from the local symmetry of the inverse image by the Hopf fibration of a real hypersurface M in complex space form M m ( 4 ϵ ) . In the second, we give a complete classification of real hypersurfaces in M m ( 4 ϵ ) which satisfy the above geometric facts.

Real hypersurfaces with parallel induced almost contact structures

Zuzanna Szancer (2012)

Annales Polonici Mathematici

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Real affine hypersurfaces of the complex space ℂ n + 1 with a J-tangent transversal vector field and an induced almost contact structure (φ,ξ,η) are studied. Some properties of hypersurfaces with φ or η parallel relative to an induced connection are proved. Also a local characterization of these hypersurfaces is given.