On the analytic distributions and foliations of a Kähler manifold

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.