Variations on Gromov's open-dense orbit theorem

Charles Frances

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arXiv · 1605.05755

Variations on Gromov's open-dense orbit theorem

Charles Frances

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Abstract

We investigate several situations where the local homogeneity of a geometric structure on a dense open subset of a manifold implies the local homogeneity everywhere. This results in a strengthening of the conclusions in Gromov's open-dense orbit theorem. In particular, we show that any smooth closed 3-dimensional Lorentz manifold with a topologically transitive isometric action must be locally homogeneous.

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Charles Frances. 2016-05-18. Variations on Gromov's open-dense orbit theorem. https://arxiv.org/abs/1605.05755

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