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On totally umbilical QR-submanifolds of quaternion Kaehlerian manifolds

Published online by Cambridge University Press:  17 April 2009

Aurel Bejancu  and
Hani Reda Farran
Aurel Bejancu
Affiliation:
Department of Mathematics and Computer Science, Kuwait Unviersity, PO Box 5969, Safat 13060, Kuwait e-mail: bejancu@math-1.sci.kuniv.edu.kwfarran@math-1.sci.kuniv.edu.kw
Hani Reda Farran
Affiliation:
Department of Mathematics and Computer Science, Kuwait Unviersity, PO Box 5969, Safat 13060, Kuwait e-mail: bejancu@math-1.sci.kuniv.edu.kwfarran@math-1.sci.kuniv.edu.kw
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Abstract

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We introduce the notion of generalised 3-Sasakian structure on a manifold and show that a totally umbilical, but not totally geodesic, proper QR-submanifold of a quaternion Kaehlerian manifold is an extrinsic sphere and inherits such a structure.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 1 , August 2000 , pp. 95 - 103
Copyright
Copyright © Australian Mathematical Society 2000

References

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