Singular Riemannian foliations on simply connected spaces
نویسندگان
چکیده
منابع مشابه
3 Singular Riemannian Foliations with Sections ∗
A singular foliation on a complete riemannian manifold is said to be riemannian if every geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. In this paper we study singular riemannian foliations that have sections, i.e., totally geodesic complete immersed submanifolds that meet each leaf orthogonally and whose dimensions are the codimensions of th...
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We prove that if the normal distribution of a singular riemannian foliation is integrable, then each leaf of this normal distribution can be extended to be a complete immersed totally geodesic submanifold (called section), which meets every leaf orthogonally. In addition the set of regular points is open and dense in each section. This result generalizes a result of Boualem and solves a problem...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2006
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2005.12.005