Point leaf maximal singular Riemannian foliations in positive curvature |
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Institution: | Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA |
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Abstract: | We generalize the notion of fixed point homogeneous isometric group actions to the context of singular Riemannian foliations. We find that in some cases, positively curved manifolds admitting these so-called point leaf maximal SRF's are diffeo/homeomorphic to compact rank one symmetric spaces. In all cases, manifolds admitting such foliations are cohomology CROSSes or finite quotients of them. Among non-simply connected manifolds, we find examples of such foliations which are non-homogeneous. |
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