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On totally umbilical QR-submanifolds of quaternion Kaehlerian manifolds

2000
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Bulletin of the Australian Mathematical Society
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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. where v L is the complementary orthogonal vector bundle to v in TM L . If in particular, v = TM L or v -{0} we say that M becomes a quaternionic submanifold (see Chen [6]) or an anti-quaternionic submanifold (see Pak [10]). In the case M is a real

doi:10.1017/s0004972700018517
fatcat:u2gr4bkzazd6lmaszimc27j5di