Foliations on Riemannian Manifolds and Submanifolds

Focusing on Riemannian geometry, this monograph explores foliations with nonnegative mixed curvature and the geometry of submanifolds featuring rulings in spaces of nonnegative curvature. It presents a decomposition approach for foliated manifolds when leaf dimensions are large. The work is structured into two parts, encompassing seven chapters and three appendices, with the first part detailing foundational results on foliated smooth manifolds and emphasizing the significance of Riemannian curvature in understanding these structures.