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Real hypersurfaces in the complex quadric with Killing normal Jacobi operator

Part of: Global differential geometry

Published online by Cambridge University Press:  27 December 2018

Young Jin Suh
Young Jin Suh*
Affiliation:
Department of Mathematics and Research Institute of Real & Complex Manifolds, College of Natural Sciences, Kyungpook National University, Daegu 41566 Republic of Korea (yjsuh@knu.ac.kr)
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Abstract

We introduce the notion of Killing normal Jacobi operator for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2. The Killing normal Jacobi operator implies that the unit normal vector field N becomes 𝔄-principal or 𝔄-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in Qm = SOm+2/SOmSO2 with Killing normal Jacobi operator.

Keywords

killing normal Jacobi operator𝔄-isotropic𝔄-principalKähler structurecomplex conjugationcomplex quadric

MSC classification

Primary: 53C40: Global submanifolds
Secondary: 53C55: Hermitian and Kählerian manifolds
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 2 , April 2019 , pp. 279 - 296
Copyright
Copyright © Royal Society of Edinburgh 2018 

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