Questions tagged [geometric-structures]
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16 questions
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Rigidity/flexibility of Sol-structures on closed 3-manifolds
This is a follow-up to the question
Rigidity/flexibility of Nil-, Sol-, $\widetilde{\rm SL}_2$- structures on closed 3-manifolds
From the answers/comments there and from an excellent survey by Bonahon ...
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7
votes
1
answer
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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 ...
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6
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2
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How to learn intrinsic torsion
I want to learn about G-structure and intrinsic torsion. But I can find no textbook that details it.
If you can give me a reference about it, it would be much appreciated.
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4
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1
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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 ...
0
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1
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Curvature tensor of interpolation of two metrics
Let $\hat{g}$ and $\bar{g}$ be two smooth Riemannian metrics defined, say, on $\mathbb{R}^n.$ Consider a smooth function $\xi$ that acts as an interpolation function between the two metrics above on ...
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9
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1
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A name for a mathematical structure of geometric type
I am looking for (maybe existing) name for a mathematical structure $(X,\leqslant)$ consisting of a set $X$ and a transitive relation ${\leqslant}\subseteq X^2\times X^2$ such that $xx\leqslant yz\...
- 41.8k
1
vote
1
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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}(...
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3
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0
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Failure of the Jacobi identity
So I'm facing a problem of physical origin which I'd like to understand on a geometric background.
I have a long, tedious bivector involving functional derivatives. I write what it would be the ...
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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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2
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1
answer
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Gromov Geometric Structures and Killing fields
Let's fix some notations: $M$ will denote a real smooth, $m$-dimensional, manifold, $F^k(M)$ is the k-th order frame bundle on $M$ and $Gl^k(m)$ is the space of $k$-jets of diffeomorphisms of $\mathbb ...
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5
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2
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What criteria are there to determine if two projective varieties are projectively equivalent?
A projective transformation is a morphism of $P^n$ to $P^n$, for some $n$, determined by an $(n + 1) \times (n + 1)$ invertible matrix $A$ in the obvious way. The sets $Q$, $R$ are projectively ...
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10
votes
1
answer
634
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necessary and sufficient condition for existence of $SU(3)$-structure on 6-manifolds
Is there any necessary and sufficient condition for existence of $SU(3)$-structure on 6-manifolds $M$?
user21574
37
votes
3
answers
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"Softness" vs "rigidity" in Geometry
According to common wisdom, there are structures in Geometry that have a more "topological" flavor, others that are more "geometrical", and others that are halfway between. Usually,...
- 23.3k
0
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1
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Non Smooth K3 surface?
Hi,
My question is related to Algebraic Surfaces. I have seen that we always consider K3 surfaces which are smooth, but I wonder how can we define a non-smooth K3 surface.
The problem I see is on ...
2
votes
2
answers
243
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Of what kind of complemented bounded poset are the structures in my quasi-variety?
I feel that my question is very basic, but, somewhat suprisingly, nobody was able to give me an answer so far:
Let
$\mathbf{M} := \langle \{ 0,1 \}, 0, 1, \leq, \neg \rangle$
be the structure with ...
- 1,498
9
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5
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Möbius and projective 3-manifolds
A projective 3-manifold is a smooth manifold that admits an atlas with values in the real projective 3-space such that all transition maps are restrictions of projective transformations. A Möbius 3-...
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