4-Dimensional Geometries |

**In General**

* __Results__: There are
pairs of homeomorphic, non-diffeomorphic smooth 4-manifolds, in which one
manifold admits an Einstein metric and the other does not, or they admit
Einstein metrics with opposite signs of *R*; There are simply connected
4-manifolds for which the space of *R* > 0 Riemannian metrics
is disconnected.

@ __Differentiable structure and metric__: Kotschick G&T(98)m.DG [homeomorphic manifolds and Einstein metrics].

@ __Riemannian__:
Karlhede CQG(88) [classification];
Kapovich JDG(04) [conformally flat].

@ __Other topics__: Ruberman G&T(01)m.DG [*R* > 0 and diffeomorphisms].

> __Online resources__:
see MathWorld page;
Wikipedia page.

**4D Lorentzian Geometry ** > s.a. lorentzian geometry;
types of metrics.

@ __General references__: Grant & Vickers CQG(09)-a0809 [block diagonalisation].

@ __Classification__: Karlhede GRG(80);
Milson & Pelavas CQG(08)-a0710 [type N].

> __Physics applications__:
see general relativity; spacetime.

**Special Cases** > see differentiable manifolds [exotic 4-spheres];
euclidean geometry [4D euclidean geomery].

main page
– abbreviations
– journals – comments
– other sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 1 jan 2016