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
- 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
1-manifolds
- Circle, S1
- Long line
- Real line, R
- Real projective line, RP1 ≅ S1
2-manifolds
- 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
- 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
- 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
Manifolds related to spheres
Special classes of Riemannian manifolds
Categories of manifolds
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The Wikibook Topology has a page on the topic of: Categories of Manifolds |
Manifolds definable by a particular choice of atlas
Manifolds with additional structure
Infinite-dimensional manifolds
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