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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


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Volume 12, Issue 12

Issues

Volume 13 (2015)

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

Eunmi Pak / Young Suh
Published Online: 2014-07-20 | DOI: https://doi.org/10.2478/s11533-014-0447-5

Abstract

Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$\mathfrak{D}^ \bot$$-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 $$\mathfrak{D}^ \bot$$-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.

MSC: 53C40; 53C15

Keywords: Complex two-plane Grassmannian; Hopf hypersurface; Generalized Tanaka-Webster connection; Structure Jacobi operator

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About the article

Published Online: 2014-07-20

Published in Print: 2014-12-01


Citation Information: Open Mathematics, Volume 12, Issue 12, Pages 1840–1851, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-014-0447-5.

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© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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