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arxiv: math/0509258 · v1 · submitted 2005-09-12 · 🧮 math.DG

Singular Riemannian Foliations on Nonpositively Curved Manifolds

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keywords manifoldsriemanniansingularadmittingfoliationsproperactionaddition
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We prove the nonexistence of a proper singular Riemannian foliation admitting section in compact manifolds of nonpositive curvature. Then we give a global description of proper singular Riemannian foliations admitting sections on Hadamard manifolds. In addition by using the theory of taut immersions we provide a short proof of this result in the special case of a polar action.

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