کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4658128 | 1633081 | 2016 | 39 صفحه PDF | دانلود رایگان |
It is proved that the isometry classes of pointed connected complete Riemannian n -manifolds form a Polish space, M⁎∞(n), with the topology described by the C∞C∞ convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifold. The locally non-periodic manifolds define an open dense subspace M⁎,lnp∞(n)⊂M⁎∞(n), which becomes a C∞C∞ foliated space with the restriction of the canonical partition. Its leaves without holonomy form the subspace M⁎,np∞(n)⊂M⁎,lnp∞(n) defined by the non-periodic manifolds. Moreover the leaves have a natural Riemannian structure so that M⁎,lnp∞(n) becomes a Riemannian foliated space, which is universal among all sequential Riemannian foliated spaces satisfying certain property called covering-determination. M⁎,lnp∞(n) is used to characterize the realization of complete connected Riemannian manifolds as dense leaves of covering-determined compact sequential Riemannian foliated spaces.
Journal: Topology and its Applications - Volume 198, 1 February 2016, Pages 47–85