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

Theoharis Theofanidis

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Displaying similar documents to “Real hypersurfaces with pseudo-𝔻-parallel structure Jacobi operator in complex hyperbolic spaces”

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 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.

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $𝔇^{⊥}$ -parallel structure Jacobi operator

Eunmi Pak, Young Suh (2014)

Open Mathematics

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Regarding the generalized Tanaka-Webster connection, we considered a new notion of $𝔇^{⊥}$ -parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂm+2) and proved that a real hypersurface in G 2(ℂm+2) with generalized Tanaka-Webster $𝔇^{⊥}$ -parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP n in G 2(ℂm+2), where m = 2n.

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.

Zolotarev's proof of Gauss reciprocity and Jacobi symbols

Szyjewski, Marek (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 11A15. We extend to the Jacobi symbol Zolotarev's idea that the Legendre symbol is the sign of a permutation, which leads to simple, strightforward proofs of many results, the proof of the Gauss Reciprocity for Jacobi symbols including.

Real hypersurfaces in quaternionic space forms.

Jürgen Berndt (1991)

Journal für die reine und angewandte Mathematik

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End-to-end gluing of constant mean curvature hypersurfaces

Mohamed Jleli (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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It was observed by R. Kusner and proved by J. Ratzkin that one can connect together two constant mean curvature surfaces having two ends with the same Delaunay parameter. This gluing procedure is known as a “end-to-end connected sum”. In this paper we generalize, in any dimension, this gluing procedure to construct new constant mean curvature hypersurfaces starting from some known hypersurfaces.

Isoparametric Hypersurfaces in the Pseudo-Riemannian Space Forms.

Jörg Hahn (1984)

Mathematische Zeitschrift

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A note on a theorem of Griffiths on the Abel-Jacobi map.

T. Shioda (1985)

Inventiones mathematicae

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On the quadric CMC spacelike hypersurfaces in Lorentzian space forms

Cícero P. Aquino, Henrique F. de Lima, Fábio R. dos Santos (2016)

Colloquium Mathematicae

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We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.