Displaying similar documents to “Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition”

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...

A characterization of totally η -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form

Mayuko Kon (2008)

Czechoslovak Mathematical Journal

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We give a characterization of totally η -umbilical real hypersurfaces and ruled real hypersurfaces of a complex space form in terms of totally umbilical condition for the holomorphic distribution on real hypersurfaces. We prove that if the shape operator A of a real hypersurface M of a complex space form M n ( c ) , c ≠ 0 , n ≥ 3 , satisfies g ( A X , Y ) = a g ( X , Y ) for any X , Y ∈ T 0 ( x ) , a being a function, where T 0 is the holomorphic distribution on M , then M is a totally η -umbilical real hypersurface or locally congruent to a ruled real...

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.