Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator
Juan de Dios Pérez; Young Jin Suh; Changhwa Woo
Open Mathematics (2015)
- Volume: 13, Issue: 1, page 313-321
- ISSN: 2391-5455
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topJuan de Dios Pérez, Young Jin Suh, and Changhwa Woo. "Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator." Open Mathematics 13.1 (2015): 313-321. <http://eudml.org/doc/271795>.
@article{JuandeDiosPérez2015,
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.},
author = {Juan de Dios Pérez, Young Jin Suh, Changhwa Woo},
journal = {Open Mathematics},
keywords = {Real hypersurfaces; Complex hyperbolic two-plane Grassmannians; Commuting shape operator; real hypersurfaces; complex two-plane Grassmannians; Hopf hypersurface; generalized Tanaka-Webster connection; recurrent shape operator},
language = {eng},
number = {1},
pages = {313-321},
title = {Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator},
url = {http://eudml.org/doc/271795},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Juan de Dios Pérez
AU - Young Jin Suh
AU - Changhwa Woo
TI - Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 313
EP - 321
AB - 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.
LA - eng
KW - Real hypersurfaces; Complex hyperbolic two-plane Grassmannians; Commuting shape operator; real hypersurfaces; complex two-plane Grassmannians; Hopf hypersurface; generalized Tanaka-Webster connection; recurrent shape operator
UR - http://eudml.org/doc/271795
ER -
References
top- [1] J. Berndt and Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatshefte für Math. 127 (1999), 1–14. Zbl0920.53016
- [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). Zbl1262.53046
- [3] P.B. Eberlein, Geometry of nonpositively curved manifolds, University of Chicago Press, Chicago, London 7, 1996. Zbl0883.53003
- [4] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Graduate Studies in Math., Amer. Math. Soc. 34, 2001.
- [5] S. Helgason, Geometric analysis on symmetric spaces, The 2nd Edition, Math. Survey and Monographs, Amer. Math. Soc. 39, 2008. Zbl1157.43003
- [6] Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. Austral. Math. Soc. 67 (2003), 493–502. [WoS] Zbl1038.53059
- [7] Y.J. Suh, Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians, Adv. Appl. Math. 50 (2013), 645-659. [WoS] Zbl1279.53051
- [8] Y.J. Suh, Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb vector field, Adv. Appl. Math. 55 (2014), 131–145. [WoS] Zbl1296.53123
- [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. [WoS] Zbl1307.53043
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