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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

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1615-7168
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𝔇-parallel normal Jacobi operators for Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster connection

Eunmi Pak / Young Jin Suh
Published Online: 2019-07-04 | DOI: https://doi.org/10.1515/advgeom-2019-0012

Abstract

We study classifying problems for real hypersurfaces in a complex two-plane Grassmannian G2(ℂm+2). In relation to the generalized Tanaka–Webster connection, we consider a new concept of parallel normal Jacobi operator for real hypersurfaces in G2(ℂm+2) and prove that a real hypersurface in G2(ℂm+2) with generalized Tanaka–Webster 𝔇-parallel normal Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍPn in G2(ℂm+2), where m = 2n.

Keywords: Real hypersurface; complex two-plane Grassmannian; Hopf hypersurface; generalized Tanaka–Webster connection; normal Jacobi operator; generalized Tanaka–Webster parallel normal Jacobi operator

MSC 2010: Primary 53C40; Secondary 53C15

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About the article

Received: 2017-03-06

Revised: 2018-03-10

Published Online: 2019-07-04


Communicated by: P. Eberlein

Funding: This research was supported by Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2017R1A6A3A01012821) and the second author by grant Proj. No. NRF-2018-R1D1A1B-05040381 from the National Research Foundation of Korea.


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0012.

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