Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster \[\mathfrak {D}^ \bot \]
-parallel structure Jacobi operator

Eunmi Pak; Young Suh

Displaying similar documents to “Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $𝔇^{⊥}$ -parallel structure Jacobi operator”

On the structure vector field of a real hypersurface in complex two-plane Grassmannians

Carlos Machado, Juan Pérez (2012)

Open Mathematics

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Considering the notion of Jacobi type vector fields for a real hypersurface in a complex two-plane Grassmannian, we prove that if a structure vector field is of Jacobi type it is Killing. As a consequence we classify real hypersurfaces whose structure vector field is of Jacobi type.

Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type

Carlos Machado, Juan Dios Pérez, Imsoon Jeong, Young Suh (2011)

Open Mathematics

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We prove the non-existence of real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type.

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

Hyunjin Lee, Juan de Dios Pérez, Young Jin Suh (2010)

Czechoslovak Mathematical Journal

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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.

Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

Konstantina Panagiotidou, Juan de Dios Pérez (2015)

Open Mathematics

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In this paper three dimensional real hypersurfaces in non-flat complex space forms whose k-th Cho operator with respect to the structure vector field ξ commutes with the structure Jacobi operator are classified. Furthermore, it is proved that the only three dimensional real hypersurfaces in non-flat complex space forms, whose k-th Cho operator with respect to any vector field X orthogonal to structure vector field commutes with the structure Jacobi operator, are the ruled ones. Finally,...

Real hypersurfaces with pseudo-𝔻-parallel structure Jacobi operator in complex hyperbolic spaces

Theoharis Theofanidis (2014)

Colloquium Mathematicae

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The aim of the present paper is to classify real hypersurfaces with pseudo-𝔻-parallel structure Jacobi operator, in non-flat complex space forms.

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 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...

On the Ricci tensor of real hypersurfaces of quaternionic projective space.

de Dios Perez, Juan (1996)

International Journal of Mathematics and Mathematical Sciences

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On real hypersurfaces in quaternionic projective space with $𝒟^{⊥}$ -recurrent second fundamental tensor.

Suh, Young Jin, Pérez, Juan de Dios (1999)

International Journal of Mathematics and Mathematical Sciences

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Displaying similar documents to “Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster 𝔇 ⊥ -parallel structure Jacobi operator”

Displaying similar documents to “Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $𝔇^{⊥}$ -parallel structure Jacobi operator”