• global hyperbolicity is a certain condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold). It is called hyperbolic...
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  • manifolds. Causality conditions Globally hyperbolic manifold Hyperbolic partial differential equation Orientable manifold Spacetime The Clockwork Rocket...
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  • Causality conditions (category Lorentzian manifolds)
    continuous Causally simple Globally hyperbolic Given are the definitions of these causality conditions for a Lorentzian manifold ( M , g ) {\displaystyle...
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  • Riemannian manifold. Ricci-flat manifolds are a special kind of Einstein manifold. In theoretical physics, Ricci-flat Lorentzian manifolds are of fundamental...
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  • Thumbnail for Manifold
    gave rise to hyperbolic geometry and elliptic geometry. In the modern theory of manifolds, these notions correspond to Riemannian manifolds with constant...
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  • Causal structure (category Lorentzian manifolds)
    Cauchy surface Closed timelike curve Cosmic censorship hypothesis Globally hyperbolic manifold Malament–Hogarth spacetime Null infinity Penrose diagram Penrose–Hawking...
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  • Thumbnail for Hyperbolic geometry
    model Constructions in hyperbolic geometry Hjelmslev transformation Hyperbolic 3-manifold Hyperbolic manifold Hyperbolic set Hyperbolic tree Kleinian group...
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  • Thumbnail for Differentiable manifold
    terms, a differentiable manifold is a topological manifold with a globally defined differential structure. Any topological manifold can be given a differential...
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  • In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a...
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  • equations, the stable manifold theorem is an important result about the structure of the set of orbits approaching a given hyperbolic fixed point. It roughly...
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  • depend on the choice of the unit vector X {\displaystyle X} . The manifold is called globally Osserman if the spectrum depends neither on X {\displaystyle...
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  • Green’s functions of Lorentzian Green hyperbolic 2nd order partial differential equations in a globally hyperbolic manifold, and in the definition of Hadamard...
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  • Thumbnail for Differential geometry
    geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of single variable calculus, vector calculus,...
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  • Thumbnail for Shape of the universe
    infinitely extended saddle shape. There are a great variety of hyperbolic 3-manifolds, and their classification is not completely understood. Those of...
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  • Thumbnail for Spacetime topology
    0). Hyperbolic rotation of the plane does not mingle the quadrants, in fact, each one is an invariant set under the unit hyperbola group. 4-manifold Clifford-Klein...
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  • Thumbnail for Riemann surface
    function-theoretic classification but it is hyperbolic in the geometric classification. Dessin d'enfant Kähler manifold Lorentz surface Mapping class group Serre...
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  • Thumbnail for Thurston's 24 questions
    Thurston in his influential 1982 paper Three-dimensional manifolds, Kleinian groups and hyperbolic geometry published in the Bulletin of the American Mathematical...
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  • metric space Completion Complex hyperbolic space Conformal map is a map which preserves angles. Conformally flat a manifold M is conformally flat if it is...
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  • Thumbnail for Yvonne Choquet-Bruhat
    development is called a globally hyperbolic vacuum development. Choquet-Bruhat also proved a uniqueness theorem: Given any two globally hyperbolic vacuum developments...
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  • Uniformization theorem (category Manifolds)
    orientable Riemannian 2-manifolds into elliptic/parabolic/hyperbolic cases. Each such manifold has a conformally equivalent Riemannian metric with constant...
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  • Latent space (redirect from Latent manifold)
    feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another...
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  • Thumbnail for Orbifold
    Orbifold (category Generalized manifolds)
    of Three-Manifolds. Princeton University lecture notes. Thurston, William (1982). "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry"...
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  • Thumbnail for Dynamical system
    manifolds of the dynamical system; they behave physically under small perturbations; and they explain many of the observed statistics of hyperbolic systems...
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  • Thumbnail for Diffeomorphism
    is an isomorphism of differentiable manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function...
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  • Thumbnail for Lagrangian coherent structure
    referred to as hyperbolic LCSs, as they provide a finite-time generalization of the classic concept of normally hyperbolic invariant manifolds in dynamical...
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  • globally hyperbolic manifold X = R × M {\displaystyle X=\mathbb {R} \times M} . Since any oriented three-dimensional manifold is parallelizable, a globally hyperbolic...
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  • studying systolic invariants of manifolds and polyhedra. Systolic hyperbolic geometry the study of systoles in hyperbolic geometry. Contents:  Top A B C...
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  • Dehn surgery (category 3-manifolds)
    given 3-manifold might be related. The answer is called the Kirby calculus. Hyperbolic Dehn surgery Tubular neighborhood Surgery on manifolds, in the...
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  • a pseudo-Riemannian manifold. On a Riemannian manifold it is an elliptic operator, while on a Lorentzian manifold it is hyperbolic. The Laplace–de Rham...
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  • 3-manifolds: of the 8 geometries, all but hyperbolic are quite constrained. Dimension 0 is trivial and 1 is straightforward. Low dimension manifolds (dimensions...
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