List of manifolds
Appearance
(Redirected from Categories of manifolds)
This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see Category:Manifolds and its subcategories.
Generic families of manifolds
[edit]- Euclidean space, Rn
- n-sphere, Sn
- n-torus, Tn
- Real projective space, RPn
- Complex projective space, CPn
- Quaternionic projective space, HPn
- Flag manifold
- Grassmann manifold
- Stiefel manifold
Lie groups provide several interesting families. See Table of Lie groups for examples. See also: List of simple Lie groups and List of Lie group topics.
Manifolds of a specific dimension
[edit]1-manifolds
[edit]- Circle, S1
- Long line
- Real line, R
- Real projective line, RP1 ≅ S1
2-manifolds
[edit]- Cylinder, S1 × R
- Klein bottle, RP2 # RP2
- Klein quartic (a genus 3 surface)
- Möbius strip
- Real projective plane, RP2
- Sphere, S2
- Surface of genus g
- Torus
3-manifolds
[edit]- 3-sphere, S3
- 3-torus, T3
- Poincaré homology sphere
- SO(3) ≅ RP3
- Solid Klein bottle
- Solid torus
- Whitehead manifold
- Meyerhoff manifold
- Weeks manifold
For more examples see 3-manifold.
4-manifolds
[edit]- Complex projective plane
- Del Pezzo surface
- E8 manifold
- Enriques surface
- Exotic R4
- Hirzebruch surface
- K3 surface
For more examples see 4-manifold.
Special types of manifolds
[edit]Manifolds related to spheres
[edit]Special classes of Riemannian manifolds
[edit]- Einstein manifold
- G2 manifold
- Kähler manifold
- Quaternionic Kähler manifold
- Riemannian symmetric space
- Spin(7) manifold
Categories of manifolds
[edit]![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png)
The Wikibook Topology has a page on the topic of: Categories of Manifolds
Manifolds definable by a particular choice of atlas
[edit]- Affine manifold
- Analytic manifold
- Complex manifold
- Differentiable (smooth) manifold
- Piecewise linear manifold
- Lipschitz manifold
- Topological manifold
Manifolds with additional structure
[edit]- Almost complex manifold
- Almost symplectic manifold
- Calibrated manifold
- Complex manifold
- Contact manifold
- CR manifold
- Finsler manifold
- Hermitian manifold
- Hyperkähler manifold
- Kähler manifold
- Lie group
- Pseudo-Riemannian manifold
- Riemannian manifold
- Sasakian manifold
- Spin manifold
- Symplectic manifold
Infinite-dimensional manifolds
[edit]See also
[edit]- List of topological spaces – List of concrete topologies and topological spaces