All Questions
Tagged with compactification conformal-geometry
5 questions
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Resources/explanations for conformal geometry with “null cones at infinity”
In the Wikipedia article on conformal geometry https://en.m.wikipedia.org/wiki/Conformal_geometry there’s a section in Mobius geometry that says it’s the study of pseudo Euclidean spaces with either a ...
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conformal compactification $\overline G$
Construct a conformal compactification, $\overline G$ of $G:=\Bbb R^{1,1}_{\gt 0}$ and/or provide a diagram of the conformal compactification of $G?$
conformal compactification
Let $G$ have the ...
- 204
3
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Point compactification of $\mathbb{R}^2$ into $\mathbb{S}^2$
Question : How to show that $(\mathbb{R}^2,\delta)$ is conformal related with $(\mathbb{S}^2,\sigma)$ ? Here we have
1.1) $\delta$ is just the standard euclidian metric in spherical coordinates;
1.2) ...
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Trying to better understand conformally compactified Euclidean space into the unit ball
Goal: To gain a better understanding of Euclidean space, $\Bbb R^3,$ conformally compactified into a unit sphere.
Question: How can I visualise and mathematically describe Euclidean space, $\Bbb R^...
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Calculation to show $|\mathrm{d}r|^2_{\bar g} = 1$ implies sectional curvatures tend to $-1$.
$\textbf{tl;dr:}$ Given that $r$ is a definining function for the boundary of a conformally compact manifold, how does one show that the sectional curvatures tend to $-1$ if $|\mathrm{d}r|^2_{\bar g} =...
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