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10 questions
24
votes
5
answers
4k
views
Weitzenböck Identities
I asked this question at Maths Stack Exchange, but I haven't received any replies yet (I'm not sure how long I should wait before it is acceptable to ask here, assuming there is such a period of time)....
- 2,821
8
votes
2
answers
489
views
Continuous point map for spherical domains
Consider the space $J$ of Jordan domains on the sphere $\textbf{S}^2$, i.e., continuous injective maps from the unit disk into $\textbf{S}^2$ modulo homeomorphisms of the disk. How can one construct a ...
- 7,149
7
votes
2
answers
436
views
Are square tiled surfaces dense in the moduli space of translation surfaces?
I'm reading the survey "An introduction to Veech surfaces" by Pascal Hubert and Thomas Schmidt.
At page 19 they state "In any fixed stratum, the set of square-tiled surfaces of that stratum is dense....
- 111
2
votes
1
answer
730
views
Vafa's semi-Ricci flat metric
Cumrun Vafa with Greene-Shapere-Yau introduced semi-Ricci flat metric here
B. Greene, A. Shapere, C. Vafa, and S.-T. Yau. Stringy cosmic strings and
noncompact Calabi-Yau manifolds. Nuclear Physics B,...
- 6,871
7
votes
2
answers
243
views
Length of simple closed curve in half-translation surface
Let $R$ be a Riemann surface of genus $g\ge 2$ and $q$ an holomorphic quadratic differential on $R$. Together they determine a semi-translation structure: an atlas on $X$ such that its changes of ...
- 15.4k
11
votes
2
answers
3k
views
Riemannian metrics as sections of a vector bundle
Let $\pi \colon E \to M$ be a smooth vector bundle. A Riemannian metric on $E$ can be regarded as a global section of the vector bundle $(E\otimes E)^{\ast}$, or more specifically, the subbundle $(S^...
CommunityBot
- 1
2
votes
1
answer
489
views
An identity for Futaki-Donaldson invariant
Let $(X,L)$ be a polarized projective variety
Given an ample line bundle $L\to X$, then a test configuration for the pair $(X,L)$ consists of :
a scheme $\mathfrak X$ with a $\mathbb C^*$-action
a ...
CommunityBot
- 1
3
votes
1
answer
266
views
Are harmonic maps quasiconformal at the boundary of hyperbolic spaces?
Let $M$ be a hyperbolic $3$-manifold and $X$ a negatively curved, simply connected space with geometric boundary $\partial X$.
If $\rho:\pi_1M\rightarrow Isom(X)$ does not fix a point in $\partial X$,...
- 31.2k
9
votes
2
answers
1k
views
Weitzenböck Identity for $\Delta_{\bar{\partial}_E}$
This question is related to this MO question and this MSE question.
Let $E$ be a hermitian holomorphic vector bundle over a hermitian manifold $X$. The bundle $\bigwedge^{\bullet,\bullet}X\otimes E$ ...
CommunityBot
- 1
11
votes
2
answers
2k
views
Non-Kahler Complex manifolds
For a non-Kahler complex manifold $M$, we still have the decomposition of differential forms into differential forms of type $(p,q)$ and we can write $d=\partial+\bar\partial$ and we can define ...
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