All Questions
Tagged with geometric-structures lie-groups
4 questions
7
votes
1
answer
190
views
Rigidity/flexibility of Nil-, Sol-, $\widetilde{\rm SL}_2$- structures on closed 3-manifolds
It is known that closed spherical and hyperbolic 3-manifolds are rigid. I.e., if two such manifolds are diffeomorphic, then they are isometric (moreover, I think, that every diffeomorphism is isotopic ...
- 353
4
votes
1
answer
235
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If a discrete and faithful representation of a surface group has proximal values, does the attracting points map have a continuous extension?
For some context, I'm studying the paper Anosov Representations and Proper Actions [GGKW].
$G$ denotes a non-compact real reductive Lie group of rank greater than $1$, $\Gamma$ denotes the fundamental ...
1
vote
1
answer
372
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What is the relationship between $\mathrm{SO}(2)$ and $\mathrm{PSL}(2,\mathbb{R})$?
$\DeclareMathOperator\SO{SO}\DeclareMathOperator\PSL{PSL}\DeclareMathOperator\R{\mathbb{R}}$The holonomy of a hyperbolic surface $S$ in terms of differential geometry is either $\SO(2)$ or $\mathrm{O}(...
- 23
5
votes
1
answer
240
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Why is generalised complex structure defined to be a reduction of structure group to $O(n,n) \cap Gl(n,\mathbb{C})$?
It is a basic and "intuition request" question. I have asked it on StackExchange yet it is probably to specialized for it since there were no answears.
Generalised complex structure is defined to be ...
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