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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: snagai@edu.toyama-u.ac.jp
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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

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