Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606382 | Differential Geometry and its Applications | 2011 | 20 Pages |
Abstract
We present short proofs of all known topological properties of general Busemann G-spaces (at present no other property is known for dimensions more than four). We prove that all small metric spheres in locally G-homogeneous Busemann G-spaces are homeomorphic and strongly topologically homogeneous. This is a key result in the context of the classical Busemann conjecture concerning the characterization of topological manifolds, which asserts that every n-dimensional Busemann G-space is a topological n-manifold. We also prove that every Busemann G-space which is uniformly locally G-homogeneous on an orbal subset must be finite-dimensional.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
V.N. Berestovskiǐ, Denise M. Halverson, Dušan Repovš,