All Questions
Tagged with dg.differential-geometry lorentzian-geometry
64 questions
4
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0
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244
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Harmonic maps into de Sitter Space
I am looking some references on the existence and non-existence of (space-like) harmonic maps solving the Dirichlet into the de-Sitter space.
More precisely: Let, for $n\geq 3$,
$$dS^n=\{ u\in \...
- 914
2
votes
1
answer
313
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$(M,g)$ is complete iff $(\tilde{M},\tilde{g})$ is complete (non-Riemannian version)
I'm not sure if this question is too low level for Math Overflow (so feel free to move this to SE if you think it is).
Inspired by this and this question I'm wondering if the following statement is ...
- 123
1
vote
0
answers
218
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Are there Lorentzian complex manifolds?
Quick and simple...
Is it possible to define complex structures on Lorentzian manifolds? If so, Can you point me to some example(s)?
- 690
5
votes
1
answer
187
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Decomposition of a Jacobi field along a lightlike geodesic
Consider a Lorentzian manifold of dimension $1+n$ (with $n\geq1$) and a lightlike geodesic $\gamma(t)$ on it.
One can define a Jacobi field $J(t)$ along $\gamma$ in the usual way without issues.
In ...
- 8,086
19
votes
1
answer
454
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Lorentzian analogue to Thurston geometries
Is there an analogue to the eight Thurston geometries for Lorentz metrics?
If so, how many "disctinct" geometries are there in the Lorentzian case?
And which closed 3-manifolds admit metrics which ...
- 893
9
votes
1
answer
560
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Is the set of Lorentzian metrics metrizable?
Fix a differentiable non-compact manifold $M$. Denote by $\mathrm{Lor}(M) := \{\text{Lorentzian metrics on $M$}\}.$ One can define a topology on this set via: fix any open covering $\mathcal{A}$ on $M$...
- 1,774
10
votes
1
answer
862
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On the topology induced by a Lorentzian metric
Let $(M,g)$ be a time-oriented smooth Lorentzian manifold, with Lorentzian metric $g$. In the following thread:
Lorentzian distance induced topology(a.k.a. Interval topology)
physicist @ValterMoretti ...
- 2,816
8
votes
2
answers
450
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On the causal structure of spacetimes: piecewise $C^1$, $C^k$ or $C^\infty$?
This is a more technical question but it seems that there is some confusion in the literature on the choice of curves used to define the causal relations in time-oriented Lorentz manifolds: the ...
- 8,098
2
votes
3
answers
800
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Tensor Field Decomposition in Space time
For vector fields in $R^3$ one knows that there exists a unique decomposition of vector fields in to solenoidal (divergence free) and potential parts. A generalization of this Theorem for symmetric ...
- 55
3
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0
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101
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Conformal Transformations that are Ricci Positive Invariant
Is there any known class of conformal transformations $\phi : M \to M$ of a riemannian/semi-riemanian manifold $(M,g)$ that have the property: $g$ is ricci-positive iff $\phi^* g$ ricci positive?
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- 31
2
votes
1
answer
562
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Induced connection on null hypersurfaces
I will use a local coordinate formalism here, since this is related to research in general relativity, and my supervisor only tolerates local coordinate formalisms. Plus the research papers I base my ...
- 2,792
3
votes
1
answer
259
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Reference for Bonnet Fundamental theorem of surfaces in Lorentzian spaces
I am looking for a reference for the following folklore theorem, which is the Lorentzian analogue of the Bonnet fundamental theorem of surface in Euclidean space, hyperbolic space or $3$d sphere.
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6
votes
0
answers
532
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Time-separation function on "globally hyperbolic" spacetimes with everywhere timelike boundary
It is well-known that, in globally hyperbolic spacetimes, the time separation function $\tau$ (aka Lorentzian distance function) enjoys the following property: fix a point $p$ and a point $q \in I^-(p)...
- 503
2
votes
1
answer
470
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Number of connected components of the isometry group of a simply-connected lorentzian manifold
Let $(M,g)$ be a finite-dimensional connected lorentzian manifold. Then the group $G$ of isometries of $M$ (i.e., the group of diffeomorphisms $\varphi : M \to M$ with $\varphi^* g = g$) is a Lie ...
- 33.3k