A local theorem on distributions whose mixed sectional curvature is positive (Q1897921)

In [Math. Ann. 188, 313-316 (1970; Zbl 0194.52804)] the reviewer considered foliations of a Riemannian manifold by complete totally geodesic leaves such that the sectional curvature of the plane spanned by one vector tangent to and a second orthogonal to the foliation is a positive constant \(k\). In this case he obtained an upper bound for the dimension of the leaves. In the present paper, this theorem is generalized in several respects, the most important being the weakening of the constancy condition of \(k\).