Hopf Hypersurfaces in Complex Two–plane Grassmannians with Generalized Tanaka–Webster Reeb–parallel Structure Jacobi Operator

Byung Hak Kim; Hyunjin Lee; Eunmi Pak∗

doi:10.5666/KMJ.2019.59.3.525

Article

KYUNGPOOK Math. J. 2019; 59(3): 525-535

Published online September 23, 2019

Hopf Hypersurfaces in Complex Two–plane Grassmannians with Generalized Tanaka–Webster Reeb–parallel Structure Jacobi Operator

Byung Hak Kim, Hyunjin Lee, Eunmi Pak∗

Department of Applied Mathematics and Institute of Natural Sciences, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Korea
e-mail : bhkim@khu.ac.kr
The Research Institute of Real and Complex Manifolds, Kyungpook National University, Daegu 41566, Korea
e-mail : lhjibis@hanmail.net
Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
e-mail : empak@hanmail.net

Received: December 28, 2017; Accepted: February 27, 2018

Abstract

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Abstract

In relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians and prove the non-existence of real hypersurfaces in G₂(ℂ^m+2) with generalized Tanaka-Webster parallel structure Jacobi operator.

Keywords: real hypersurface, complex two-plane Grassmannian, Hopf hypersurface, generalized Tanaka-Webster connection, structure Jacobi operator.