Singular Riemannian foliations and applications to positive and nonnegative curvature. [Preprint]
We determine the structure of the fundamental group of the regular leaves of a closed singular Riemannian foliation on a compact, simply connected Riemannian manifold. We also study closed singular Riemannian foliations whose leaves are homeomorphic to aspherical or to Bieberbach manifolds. These foliations, which we call A-foliations and B-foliations, respectively, generalize isometric torus actions on Riemannian manifolds. We apply our results to the classification problem of compact, simply connected Riemannian 4- and 5-manifolds with positive or nonnegative sectional curvature.
|Zugehörige Institution(en) am KIT
||Institut für Algebra und Geometrie (IAG)
||KITopen ID: 1000051186
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