Vol. 39, No. 2, 1971

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Almost contact manifolds with Killing structure tensors

David Blair

Vol. 39 (1971), No. 2, 285–292

An almost Hermitian manifold whose almost complex structure is Killing is called a nearly Kaehler manifold; the usual almost complex structure on the six-sphere is a wellknown example.

The purpose of this note is to introduce the study of almost contact metric manifolds whose almost contact structure tensors are Killing. In particular if such a structure is normal it is cosymplectic. Hypersurfaces of nearly Kaehler manifolds are also studied. As an example, it is shown that the five-sphere carries a nonnormal almost contact metric structure. More generally, the induced structure on a compact orientable hypersurface of a nearly Kaehler manifold of positive curvature cannot be cosymplectic.

Mathematical Subject Classification 2000
Primary: 53C15
Received: 20 August 1970
Revised: 12 April 1971
Published: 1 November 1971
David Blair