RT Journal Article
T1 A universal Riemannian foliated space
A1 Álvarez López, Jesús Antonio
A1 Barral Lijó, Ramón
A1 Candel, Alberto
K1 Locally non-periodic Riemannian manifolds
K1 Riemannian foliated space
K1 Smooth convergence of Riemannian manifolds
AB It is proved that the isometry classes of pointed connected complete Riemannian n-manifolds form a Polish space X with the topology described by the smooth 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 Y, which becomes a smooth foliated space with the restriction of the canonical partition. Its leaves without holonomy form the subspace Z defined by the non-periodic manifolds. Moreover, the leaves have a natural Riemannian structure so that Y becomes a Riemannian foliated space, which is universal among all sequential Riemannian foliated spaces satisfying certain property called covering-determination. Y is used to characterize the realization of complete connected Riemannian manifolds as dense leaves of covering-determined compact sequential Riemannian foliated spaces.
PB Elsevier
SN 0166-8641
YR 2016
FD 2016
LK http://hdl.handle.net/10347/32662
UL http://hdl.handle.net/10347/32662
LA eng
NO Álvarez López, J.A., Barral Lijó, R., Candel, A. (2016). A universal Riemannian foliated space. "Topology and its Applications", vol. 198, 47-85.
NO The first and third authors are partially supported by MICINN (Spain), grant MTM2011-25656.
DS Minerva
RD 29 abr 2026