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...he '''Clifton–Pohl torus''' is an example of a [[compact space|compact]] [[Lorentzian manifold]] that is not [[geodesically complete]]. While every compact [[Rie ...g)</math> is extendable, i.e. that it can be seen as a subset of a bigger Lorentzian surface. It is a direct consequence of a simple change of coordinates. Wit ...

...of pairs of points in a smooth [[spacetime]] <math>M</math> with smooth [[Lorentzian metric]] <math>g </math>. Let <math>x, x'</math> be two points in spacetime Obviously Synge's function can be defined also in Riemannian manifolds and in that case it has non-negative sign. ...

...n theory]], a '''world manifold''' endowed with some [[Lorentzian manifold|Lorentzian]] [[pseudo-Riemannian manifold|pseudo-Riemannian metric]] and an associated == Lorentzian structure == ...

...''X'')-structure are always [[manifold]]s and are called '''(''G'', ''X'')-manifolds'''. This notion is often used with ''G'' being a [[Lie group]] and ''X'' a ...<math>(G, X)</math> manifolds is equivalent to the category of Riemannian manifolds which are locally isometric to <math>X</math> (i.e. every point has a neigh ...

...tein equations]] of general relativity, albeit with Riemannian rather than Lorentzian [[metric signature]]. It may be regarded as a [[resolution of singularities ...

{{Short description|Vector bundle associated with conformal manifolds}} ...onditions specific to the signature). In the case of a four-dimensional [[Lorentzian manifold]], such as the space-time of general relativity, a local twistor h ...

In the theory of [[Lorentzian manifold]]s, [[spherically symmetric spacetime]]s admit a family of ''neste ...ying a [[metric tensor]] <math>g</math> is part of the definition of any [[Lorentzian manifold]]. The simplest way to define this tensor is to define it in comp ...

...''development''' of {{math|(''M'', ''g'', ''k'')}} is a four-dimensional [[Lorentzian manifold]] {{math|({{overline|''M''}}, {{overline|''g''}})}} together with ...ion of the submanifold geometry of an embedded spacelike hypersurface in a Lorentzian manifold. ...

...from flat spacetime ([[Minkowski space]]) to curved spacetime, a general [[Lorentzian manifold]]. ...ut which restricts to an ''orthonormal'' frame bundle on pseudo-Riemannian manifolds. ...

...ts that spacetime is 10-dimensional, consisting of a [[Lorentzian manifold|Lorentzian]] manifold of dimension 4 (usually assumed to be [[Minkowski space]] or [[D ...abi–Yau 3-fold <math>X</math>.<ref>Aspinwall, P.S., D-Branes on Calabi–Yau Manifolds. In Progress in String Theory: TASI 2003 Lecture Notes. Edited by MALDACENA ...

[[Category:Lorentzian manifolds]] ...

...symmetry group]] of [[Asymptotically flat spacetime|asymptotically flat]], Lorentzian [[spacetime]]s at [[Null infinity|null (''i.e.'', light-like) infinity]]. I [[Category:Lorentzian manifolds]] ...

[[Category:Lorentzian manifolds]] ...

...nifold <math>\mathcal M \in \mathcal P \times \mathcal I</math>, invariant manifolds and their associated material surfaces are abundant and generally undisting === LCSs vs. classical invariant manifolds === ...

*{{citation|last=Lawson|first=J. D.|title=Semigroups in Möbius and Lorentzian geometry|journal=Geom. Dedicata|volume= 70|issue=2|year= 1998|pages=139–180 ...ng|last= Mok|title=Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds|publisher= World Scientific|year=1989|isbn=9971-5-0802-8}} ...