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Real Hypersurfaces in Complex Two-plane Grassmannians with Reeb Parallel Ricci Tensor in the GTW Connection

Published online by Cambridge University Press:  20 November 2018

Juan de Dios Pérez ,
Hyunjin Lee ,
Young Jin Suh  and
Changhwa Woo
Juan de Dios Pérez
Affiliation:
Departamento de Geometria y Topologia, Universidad de Granada, 18071-Granada, Spain e-mail: jdperez@ugr.es
Hyunjin Lee
Affiliation:
Research Institute of Real and Complex Manifold, Kyungpook National University, Daegu 702-701, Republic of Korea e-mail: lhjibis@hanmail.net
Young Jin Suh
Affiliation:
Department of Mathematics and Research Institute of Real and Complex Manifold, Kyungpook National University, Daegu 702-701, Republic of Korea e-mail: yjsuh@knu.ac.kr
Changhwa Woo
Affiliation:
Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea e-mail: legalgwch@naver.com
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Abstract

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There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$. Among them, Suh classified Hopf hypersurfaces in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ with Reeb parallel Ricci tensor in Levi–Civita connection. In this paper, we introduce the notion of generalized Tanaka–Webster $\left( \text{GTW} \right)$ Reeb parallel Ricci tensor for Hopf hypersurfaces in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$. Next, we give a complete classification of Hopf hypersurfaces in ${{G}_{2}}\left( {{\mathbb{C}}^{m+2}} \right)$ with $\text{GTW}$ Reeb parallel Ricci tensor.

Keywords

53C4053C15complex two-plane Grassmannianreal hypersurfaceHopf hypersurfacegeneralized Tanaka-Webster connectionparallelismReeb parallelismRicci tensor
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 4 , 01 December 2016 , pp. 721 - 733
Copyright
Copyright © Canadian Mathematical Society 2016

References

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