Note on Regular K-c ntact 3-structures

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  • Note on regular K-contact 3-structures

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In a previous paper [4] we studied fibred Riemannian manifolds with Sasakian 3-structure. That is a fibred Riemannian manifold (M^^~, M, π ; g^^~) such that M^^~ has a Sasakian 3-structure and their associated 3 vector fields are tangent to each fibre π^<-1>(p) (p∈M). Then it has been shown in [2] that the base manifold M has a quaternion Kaehler structure. More generally, if M^^~ is a fibred Riemannian manifold with K-contact 3-structure, an almost quaternion structure can be induced in the base manifold. In this note, we show that if the structure induced in M is a quaternion Kaehler structure, then the K-contact 3-structure in M^^~ is necessarily Sasakian 3-structure.

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