Variations on Gromov's open-dense orbit theorem

2016/05/18 by Frances, Charles · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.05755

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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