Singular Riemannian Foliations on Nonpositively Curved Manifolds

Dirk Toeben

Singular Riemannian Foliations on Nonpositively Curved Manifolds

Differential Geometry 2007-05-23 v1

Authors: Dirk Toeben

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.

Keywords

singular Riemannian foliation nonpositive curvature compact manifold Hadamard manifold taut immersion polar action

Cite

@article{arxiv.math/0509258,
  title  = {Singular Riemannian Foliations on Nonpositively Curved Manifolds},
  author = {Dirk Toeben},
  journal= {arXiv preprint arXiv:math/0509258},
  year   = {2007}
}

Comments

10 pages

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