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
Special classes of Riemannian manifolds
- Einstein manifold
- G2 manifold
- Kähler manifold
- Quaternionic Kähler manifold
- Riemannian symmetric space
- 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
- Affine manifold
- Analytic manifold
- Complex manifold
- Differentiable (smooth) manifold
- Piecewise linear manifold
- Lipschitz manifold
- Topological manifold
Manifolds with additional structure
- 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
See also
- List of topological spaces – List of concrete topologies and topological spaces
References
- v
- t
- e
- Curve
- Diffeomorphism
- Geodesic
- Exponential map
- in Lie theory
- Foliation
- Immersion
- Integral curve
- Lie derivative
- Section
- Submersion
manifolds
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