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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Open Mathematics
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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
[2] J. Berndt and Y. J. Suh, Hypersurfaces in noncompact complex Grassmannians of rank two, International J. of Math., World Sci. Publ., 23 (2012), 1250103(35 pages). Google Scholar
[3] P.B. Eberlein, Geometry of nonpositively curved manifolds, University of Chicago Press, Chicago, London 7, 1996. Google Scholar
[4] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Graduate Studies in Math., Amer. Math. Soc. 34, 2001. Google Scholar
[5] S. Helgason, Geometric analysis on symmetric spaces, The 2nd Edition, Math. Survey and Monographs, Amer. Math. Soc. 39, 2008. Google Scholar
[6] Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. Austral. Math. Soc. 67 (2003), 493–502. Web of ScienceGoogle Scholar
[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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