Real Hypersurfaces with Invariant Normal Jacobi Operator in the Complex Hyperbolic Quadric

Imsoon Jeong; Gyu Jong Kim*

doi:10.5666/KMJ.2020.60.3.551

Article

Kyungpook Mathematical Journal 2020; 60(3): 551-570

Published online September 30, 2020

Real Hypersurfaces with Invariant Normal Jacobi Operator in the Complex Hyperbolic Quadric

Imsoon Jeong, Gyu Jong Kim*

Department of Mathematics Education, Cheongju University, Cheongju 28503, Republic of Korea
e-mail : isjeong@cju.ac.kr
Department of Mathematics Education, Woosuk University, Wanju, Jeonbuk 55338, Republic of Korea
e-mail : hb2107@naver.com

Received: March 5, 2019; Revised: May 20, 2019; Accepted: June 10, 2019

Abstract

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Abstract

We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Qm*=SOm,2o/SOmSO2. The invariant normal Jacobi operator implies that the unit normal vector field N becomes -principal or -isotropic. Then in each case, we give a complete classification of real hypersurfaces in Qm*=SOm,2o/SOmSO2 with Lie invariant normal Jacobi operators.

Keywords: invariant normal Jacobi operator, A-isotropic, A-principal, Kä,hler structure, complex conjugation, complex hyperbolic quadric.