This monograph is based on the author's results on the Riemannian
ge ometry of foliations with nonnegative mixed curvature and on the
geometry of sub manifolds with generators (rulings) in a Riemannian
space of nonnegative curvature. The main idea is that such foliated
(sub) manifolds can be decom posed when the dimension of the leaves
(generators) is large. The methods of investigation are mostly
synthetic. The work is divided into two parts, consisting of seven
chapters and three appendices. Appendix A was written jointly with
V. Toponogov. Part 1 is devoted to the Riemannian geometry of
foliations. In the first few sections of Chapter I we give a survey
of the basic results on foliated smooth manifolds (Sections
1.1-1.3), and finish in Section 1.4 with a discussion of the key
problem of this work: the role of Riemannian curvature in the study
of foliations on manifolds and submanifolds."
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