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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

Open Access
Online
ISSN
2391-5455
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Volume 13, Issue 1 (Aug 2015)

Issues

Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator

Juan de Dios Pérez / Young Jin Suh / Changhwa Woo
Published Online: 2015-08-17 | DOI: https://doi.org/10.1515/math-2015-0046

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.

Keywords: Real hypersurfaces; Complex hyperbolic two-plane Grassmannians; Commuting shape operator

References

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  • [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, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0046.

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©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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