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

• Autorzy: Juan de Dios Pérez , Young Jin Suh , Changhwa Woo
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-05-13

zaakceptowano

2015-07-15

online

2015-08-17

Twórcy

autor

Juan de Dios Pérez

• Departamento de Geometria y Topologia, Universidad de Granada, 18071-Granada, Spain

autor

Young Jin Suh

• Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic Of Korea

autor

Changhwa Woo

• Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic Of Korea

Bibliografia

• [1] J. Berndt and Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatshefte für Math. 127 (1999), 1–14.
• [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).
• [3] P.B. Eberlein, Geometry of nonpositively curved manifolds, University of Chicago Press, Chicago, London 7, 1996.
• [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.
• [6] Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator, Bull. Austral. Math. Soc. 67 (2003), 493–502. [WoS]
• [7] Y.J. Suh, Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians, Adv. Appl. Math. 50 (2013), 645-659. [WoS]
• [8] Y.J. Suh, Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb vector field, Adv. Appl. Math. 55 (2014), 131–145. [WoS]
• [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]

Identyfikatory

DOI

10.1515/math-2015-0046