alexa Locally G -homogeneous Busemann G -spaces


Journal of Generalized Lie Theory and Applications

Author(s): VN Berestovski , Denise M Halverson, DuanRepov

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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.

This article was published in Differential Geometry and its Applications and referenced in Journal of Generalized Lie Theory and Applications

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