Abstract
In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassmannians SU2.m/S(U2·Um), m≥3, whose structure tensors {ɸi}i=1,2,3 commute with the shape operator.
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Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator
Juan de Dios Pérez
- Departamento de Geometria y Topologia, Universidad de Granada, 18071-Granada, Spain
- Other articles by this author:
- De Gruyter OnlineGoogle Scholar
- Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic Of Korea
- Other articles by this author:
- De Gruyter OnlineGoogle Scholar
- Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic Of Korea
- Other articles by this author:
- De Gruyter OnlineGoogle Scholar
Published Online: 2015-08-17 | DOI: https://doi.org/10.1515/math-2015-0046
Open Access
References
[1] J. Berndt and Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatshefte für Math. 127 (1999), 1–14. Google Scholar
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[7] Y.J. Suh, Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians, Adv. Appl. Math. 50 (2013), 645—659. Web of ScienceGoogle Scholar
[8] Y.J. Suh, Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb vector field, Adv. Appl. Math. 55 (2014), 131–145. Web of ScienceGoogle Scholar
[9] Y.J. Suh and C. Woo, Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with parallel Ricci tensor, Math. Nachr. 287 (2014), 1524–1529. Web of ScienceGoogle Scholar
About the article
Received: 2015-05-13
Accepted: 2015-07-15
Published Online: 2015-08-17
Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0046.
©2015 Juan de Dios Pérez et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0
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