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Singular Riemannian foliations and applications to positive and nonnegative curvature. [Preprint]

Galaz-Garcia, Fernando; Radeschi, Marco

Abstract:
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)
Publikationstyp Buchaufsatz
Jahr 2013
Sprache Englisch
Identifikator KITopen-ID: 1000051186
Erschienen in arXiv [math.DG]
Seiten arXiv:1302.4593
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