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Naturally reductive homogeneous real hypersurfaces in quaternionic space forms

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Setsuo Nagai
Setsuo Nagai
Affiliation:
Department of Mathematics Faculty of Education Toyama University3190 Gofuku Toyamashi 930-8555Japan e-mail: [email protected]
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Abstract

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We determine the naturally reductive homogeneous real hypersurfaces in the family of curvature-adapted real hypersurfaces in quaternionic projective space HPn(n ≥ 3). We conclude that the naturally reductive curvature-adapted real hypersurfaces in HPn are Q-quasiumbilical and vice-versa. Further, we study the same problem in quaternionic hyperbolic space HHn(n ≥ 3).

Keywords

naturally reductivereal hypersurfacequaternionic space form

MSC classification

Secondary: 53C30: Homogeneous manifolds 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C40: Global submanifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 1 , February 2003 , pp. 87 - 100
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Ambrose, W. and Singer, I. M., ‘On homogeneous Riemannian manifolds’, Duke Math. J. 25 (1958), 647–669.CrossRefGoogle Scholar
[2]Berndt, J., ‘Real hypersurfaces in quaternionic space forms’, J. Reine Angew. Math. 419 (1991), 9–26.Google Scholar
[3]Berndt, J. and Vanhecke, L., ‘Naturally reductive Riemannian homogeneous spaces and real hypersurfaces in complex and quaternionic space forms’, in: Differential geometry and its applications (eds. Kowalski, O. and Krupka, D.), Math. Publ. 1 (Silesian Univ. and Open Education and Sciences, Opava, 1993) pp. 353–364.Google Scholar
[4]Ishihara, S., ‘Quaternion Kählerian manifolds’, J. Differential Geom. 9 (1974), 483–500.CrossRefGoogle Scholar
[5]Martinez, A. and Perez, J. D., ‘Real hypersurfaces in quaternionic projective space’, Ann. Mat. Pura Appl. (IV) 145 (1986), 355–384.CrossRefGoogle Scholar
[6]Pak, J. S., ‘Real hypersurfaces in quaternionic Kälerian manifolds with constant Q-sectional curvature’, Kōdai Math. Sem. Rep. 29(1977), 22–61.Google Scholar
[7]Tricerri, F. and Vanhecke, L., Homogeneous structures on Riemannian manifolds, London Math. Soc. Lecture Note Ser. 83 (Cambridge Univ. Press, Cambridge, 1983).CrossRefGoogle Scholar