The author studies polar foliations of symmetric spaces. Throughout the paper, \(M\) is a simply connected non-negatively curved symmetric space while \(\mathcal{F}\) is a polar foliation on \(M\). The main results are contained in the following theorems.
Theorem. 1.1. If \(M\) is irreducible and codim \(\mathcal{F}\geq 3\), then either the leaves are single points, or \(\mathcal{F}\) is hyperpolar, or \(M\) is of rank one:
Theorem. 1.2. One has a splitting \(M = M_{-1}\times M_0\times{M_1}\times\cdots\times M_l\), \(\mathcal{F}\) is a product of polar foliations \(\mathcal{F}_i\) on \(M_i\), \(\mathcal{F}_{-1}\) is a foliation by the fibers of the projection of \(M_{-1}\) onto a direct factor, \(\mathcal{F}_0\) is hyperpolar and, for \(i\geq 1\), the sections of \(\mathcal{F}_i\) have constant positive sectional curvature; moreover, if \(i\geq 1\) and codim \(\mathcal{F}_i\geq 3\) in \(M_i\), then \(M_i\) is irreducible and of rank one, and \(\mathcal{F}_i\) lifts to a polar foliation of a round sphere.