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Singular Riemannian foliations on nonpositively curved manifolds

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Abstract

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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  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Köln, Germany

    Dirk Töben

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  1. Dirk Töben
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Töben, D. Singular Riemannian foliations on nonpositively curved manifolds. Math. Z. 255, 427–436 (2007). https://doi.org/10.1007/s00209-006-0044-9

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  • DOI: https://doi.org/10.1007/s00209-006-0044-9

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