Abstract
In this short note we recall some results on growth of leaves of transversely affine foliations and we use these facts to formulate obstructions for open manifolds to be leaves of such foliations. Next, we demonstrate that leaves of transversely geodesically complete transversely affine foliations as well as those of Riemannian and totally geodesic foliations, have bounded homotopy property. Finally, we give some necessary conditions and discuss some open problems concerning the transverse geodesical completeness of such foliations.
Recent years have known a new interest in geometrical and topological properties leaves of a foliations. It is directly related to the question whether a given manifold can be a leaf of a (codimension one, any codimension) foliation of a compact manifold. The resolution of the question in the topological case, cf. [5, 10, 8], led to imposing some geometrical condition on the manifold, e.g. the quasi-isometry type.
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© 1999 Springer Science+Business Media Dordrecht
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Wolak, R.A. (1999). On Leaves of Transversely Affine Foliations. In: Szenthe, J. (eds) New Developments in Differential Geometry, Budapest 1996. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5276-1_35
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DOI: https://doi.org/10.1007/978-94-011-5276-1_35
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