List of manifolds
From Wikipedia, the free encyclopedia
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.
Contents
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
- 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[edit]
1-manifolds[edit]
- Real line, R
- Circle, S1
- Real projective line, RP1 ≅ S1
- Long line
2-manifolds[edit]
- 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[edit]
- 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[edit]
For more examples see 4-manifold.
Special types of manifolds[edit]
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Special classes of Riemannian manifolds[edit]
- Riemannian symmetric space
- Einstein manifold
- Kähler manifold
- Quaternionic Kähler manifold
- G2 manifold
- Spin(7) manifold
Categories of manifolds[edit]
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The Wikibook Topology has a page on the topic of: Categories of Manifolds |
See also: Category:Structures on manifolds
Manifolds definable by a particular choice of atlas[edit]
- Topological manifold
- Piecewise linear manifold
- Differentiable manifold
- Smooth manifold
- Analytic manifold
- Complex manifold
Manifolds with additional structure[edit]
- 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