List 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
- Euclidean space, Rn
- n-sphere, Sn
- n-torus, Tn
- Real projective space, RPn
- Complex projective space, CPn
- Quaternionic projective space, HPn
- Grassmann manifold
- Flag 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
1-manifolds
2-manifolds
- Sphere, S2
- Real projective plane, RP2
- Torus
- Double torus
- Möbius strip
- Klein bottle, RP2 # RP2
- Cylinder, S1 × R
- Klein quartic (a genus 3 surface)
- Surface of genus g
3-manifolds
- 3-sphere, S3
- SO(3) ≅ RP3
- 3-torus, T3
- Poincaré homology sphere
- Whitehead manifold
- Weeks manifold
- Solid torus
- Solid Klein bottle
For more examples see 3-manifold.
4-manifolds
For more examples see 4-manifold.
Special types of manifolds
Manifolds related to spheres
Special classes of Riemannian manifolds
- Riemannian symmetric space
- Einstein manifold
- Kähler manifold
- Quaternionic Kähler manifold
- G2 manifold
- Spin(7) manifold
Categories of manifolds
The Wikibook Topology has a page on the topic of: Categories of Manifolds |
Manifolds definable by a particular choice of atlas
- Topological manifold
- Piecewise linear manifold
- Differentiable manifold
- Smooth manifold
- Analytic manifold
- Complex manifold
Manifolds with additional structure
- Riemannian manifold
- Pseudo-Riemannian manifold
- Finsler manifold
- Contact manifold
- Complex manifold
- Almost complex manifold
- Symplectic manifold
- Almost symplectic manifold
- Hermitian manifold
- Kähler manifold
- Hyperkähler manifold
- Calibrated manifold
- CR manifold
- Spin manifold
- Sasakian manifold
- Lie group