Abstract.
A contact 3-structure consists of three contact metric structures which satisfy the relation (2.1). On a product manifold of the real line and a manifold with a contact 3-structure, we can construct three almost Hermitian structures satisfying the quaternionic identities. From this view point we discuss a contact 3-structure. Owing to Hitchin's well known Lemma concerning to hyperkähler structure (Lemma H), we show that a contact 3-structure is necessarily a Sasakian 3-structure.
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Received: 26 August 1999; in final form: 2 May 2000 / Published online: 4 May 2001
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Kashiwada, T. On a contact 3-structure. Math Z 238, 829–832 (2001). https://doi.org/10.1007/s002090100279
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DOI: https://doi.org/10.1007/s002090100279