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Almost Kenmotsu manifolds and nullity distributions. (English) Zbl 1204.53025

The authors study almost Kenmotsu manifolds, a certain class of almost contact metric manifolds. They show that \(\mathcal{D}\) (the kernel of the contact form) is CR-integrable (i.e. its integral manifolds are Kähler) iff there exists an invariant metric connection with torsion preserving the structure, which is then unique. Then, they investigate the relation between the Reeb vector field and certain curvature defined distributions, so-called nullity distributions, to prove CR-integrability results. The 3-dimensional case is discussed separately.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
58A30 Vector distributions (subbundles of the tangent bundles)
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