On the analytic distributions and foliations of a Kähler manifold

Vaisman, Izu

doi:10.1090/S0002-9939-1976-0428233-5

On the analytic distributions and foliations of a Kähler manifold
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Proc. Amer. Math. Soc. 58 (1976), 221-228 Request permission

Abstract:

A Frobenius-type condition involving ${d_{\bar z}}$ is proved for the analyticity of a distribution on a complex analytic manifold. As a consequence, an invariant condition for the analyticity of a distribution on a Kähler manifold is derived and used to establish the local reducibility of some foliate Kähler manifolds with bundle-like metric.

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