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A new classification on parallel Ricci tensor for real hypersurfaces in the complex quadric

Part of: Global differential geometry

Published online by Cambridge University Press:  18 November 2020

Hyunjin Lee  and
Young Jin Suh
Hyunjin Lee
Affiliation:
The Research Institute of Real and Complex Manifolds (RIRCM), Kyungpook National University, Daegu41566, Republic of Korea (lhjibis@hanmail.net)
Young Jin Suh
Affiliation:
Kyungpook National University, College of Natural Sciences, Department of Mathematics and Research Institute of Real & Complex Manifolds Daegu 41566, Republic of Korea (yjsuh@knu.ac.kr)
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Abstract

First we introduce the notion of parallel Ricci tensor ${\nabla }\mathrm {Ric}=0$ for real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2 and show that the unit normal vector field N is singular. Next we give a new classification of real hypersurfaces in the complex quadric Qm = SOm+2/SOmSO2 with parallel Ricci tensor.

Keywords

Parallel Ricci tensor$\mathfrak {A}$-isotropic$\mathfrak {A}$-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 151 , Issue 6 , December 2021 , pp. 1846 - 1868
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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