# List of manifolds

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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.

## 1-manifolds

• Real line, R
• Circle, S1
• Real projective line, RP1S1
• Long line
• ## 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
• Weeks manifold
• Solid torus
• Solid Klein bottle
• For more examples see 3-manifold.

## 4-manifolds

• Exotic R4
• E8 manifold
• For more examples see 4-manifold.

## Manifolds related to spheres

• Homology sphere
• Homotopy sphere
• Exotic sphere
• Milnor sphere
• Spherical 3-manifold
• Lens space
• ## Special classes of Riemannian manifolds

• Riemannian symmetric space
• Einstein manifold
• Ricci-flat manifold
• Kähler manifold
• Calabi–Yau manifold
• Hyperkähler manifold
• Quaternionic Kähler manifold
• G2 manifold
• Spin(7) manifold
• ## 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
• ## Infinite-dimensional manifolds

• Hilbert manifold
• Banach manifold
• Fréchet manifold
• ## References

List of manifolds Wikipedia

Topics

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