Submersions of CR-submanifolds of a Kaehler manifold (Q1114942)

Let \(\pi\) : \(M\to B\) be a submersion of a CR-submanifold M of a Kaehler manifold \(\bar M\) onto an almost Hermitian manifold B. If \(\pi\) satisfies some natural conditions, \textit{S. Kobayashi} [Tohoku Math. J., II. Ser. 39, 95-100 (1987; Zbl 0619.58004)] proved that the base manifold B is Kähler. In this article the authors study various relations between M and its base manifold B when M is assumed to be a CR-product, mixed- foliated, or totally umbilical.