Hostname: page-component-7857688df4-fwx92 Total loading time: 0 Render date: 2025-11-18T07:34:33.601Z Has data issue: false hasContentIssue false
  • English
  • Français

Real hypersurfaces in complex two-plane Grassmannians with commuting shape operator

Published online by Cambridge University Press:  17 April 2009

Young Jin Suh
Young Jin Suh
Affiliation:
Kyungpook National University, Department of Mathematics, Taegu 702-701, Korea, e-mail: yjsuh@wmail.knu.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we give a non-existence property of real hypersurfaces in complex two-plane Grassmannians G2(ℂm+2) which have a shape operator A commuting with the structure tensors {φ1, φ2, φ3}. From this view point we give a characterisation of real hypersurfaces of type B in G2(ℂm+2).

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 3 , December 2003 , pp. 379 - 393
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Berndt, J., ‘Real hypersurfaces in quaternionic space forms’, J. Reine Angew. Math. 419 (1991), 9–26.Google Scholar
[2]Berndt, J. and Suh, Y.J., ‘Real hypersurfaces in complex two-plane Grassmannians’, Monatsh. Math. 127 (1999), 1–14.CrossRefGoogle Scholar
[3]Berndt, J. and Suh, Y.J., ‘Isometric flows on real hypersurfaces in complex two-plane Grassmannians’, Monatsh. Math. 137 (2002), 87–98.CrossRefGoogle Scholar
[4]Cecil, T.E. and Ryan, P.J., ‘Focal sets and real hypersurfaces in complex projective space’, Trans. Amer. Math. Soc. 269 (1982), 481–499.Google Scholar
[5]Kimura, M., ‘Real hypersurfaces and complex submanifolds in complex projective space’, Trans. Amer. Math. Soc. 296 (1986), 137–149.CrossRefGoogle Scholar
[6]Pak, J.S., ‘Real hypersurfaces in quaternionic Kaehlerian manifolds with constant Q-sectional curvature’, Kodai Math. Sem. Rep. 29 (1977), 22–61.CrossRefGoogle Scholar
[7]Martinez, A. and Pérez, J.D., ‘Real hypersurfaces in quaternionic projective space’, Ann Mat. Pura Appl. 145 (1986), 355–384.CrossRefGoogle Scholar
[8]Yano, K. and Kon, M., CR-submanifolds of Kaehlerian and Sasakian manifolds (Birkhäuser, Boston, Basel, Strutgart, 1983).CrossRefGoogle Scholar