On the Locally Branched Euclidean Metric Gauge
نویسندگان
چکیده
A metric gauge on a set is a maximal collection of metrics on the set such that the identity map between any two metrics from the collection is locally bi-Lipschitz. We characterize metric gauges that are locally branched Euclidean and discuss an obstruction to removing the branching. Our characterization is a mixture of analysis, geometry, and topology with an argument of Yu. Reshetnyak to produce the branched coordinates for the gauge.
منابع مشابه
Assessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation
Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...
متن کاملSelf-Dual Solutions to Euclidean Gravity
The discovery of self-dual instanton solutions in Euclidean Yang-Mills theory [I] has recently stimulated a great deal of interest in self-dual solutions to Einstein’s theory of gravitation. One would expect that the relevant instanton-like metrics would be those whose gravitational fields are self-dual, localized in Euclidean spacetime and free of singularities. In fact, solutions have been fo...
متن کاملar X iv : m at h / 07 02 45 3 v 2 [ m at h . D G ] 1 6 Fe b 20 07 Locally Euclidean metrics on R 3
For all 0 < t ≤ 1, we define a locally Euclidean metric ρt on R . These metrics are invariant under Euclidean isometries and, if t increases to 1, converge to the Euclidean metric dE . This research is motivated by expanding universe. key words. locally Euclidean metric PACS number(s). 98.80.Jk Mathematics Subject Classifications (2000). 85A40, 57M50 1 The metric ρt Let dE denote the Euclidean ...
متن کاملTangent Bundle of the Hypersurfaces in a Euclidean Space
Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...
متن کاملOn the metric triangle inequality
A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.
متن کامل