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Questions tagged [geometry]

For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.

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If an immersion $X$ maps circles into planes then its image $X(\mathbb{D})$ is homeomorphic to the cylinder.

Let $X:\left( u,v\right)\in \mathbb{D}\backslash \left\{ 0\right\}\subseteq\mathbb{R}^2 \mathbb{% \longmapsto }\left( x\left( u,v\right) ,y\left( u,v\right) ,z\left( u,v\right) \right) \in \mathbb{\...
2
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What is actually the geometry or analysis behind the fact that $Mob(\hat{\Bbb C})$ is simple?

Let, $Mob(\hat{\Bbb C})$ be the group of all Mobius transformations from the extended complex plane to itself i.e. from $\hat{\Bbb C} \to \hat{\Bbb C}$ . I have been able to prove that (i) $Mob(\hat{...