Metric Flows in Space Forms of Nonpositive Curvature

We characterize those space forms of nonpositive curvature that admit one-dimensional Riemannian foliations. The hyperbolic ones are essentially the trivial line bundles over the flat ones. In particular, any such space admits a flat metric.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1995-10, Vol.123 (10), p.3177-3181
Main Authors: Basmajian, Ara, Walschap, Gerard
Format: Article
Language:English
Subjects:
Curvature
Hyperplanes
Hypersurfaces
Leaves
Mathematical constants
Mathematical theorems
Riemann manifold
Tangents
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Description
Summary:We characterize those space forms of nonpositive curvature that admit one-dimensional Riemannian foliations. The hyperbolic ones are essentially the trivial line bundles over the flat ones. In particular, any such space admits a flat metric.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-1995-1301009-4