This is a list of particular manifolds. See also list of geometric topology topics. For categorical listings see :Category:Manifolds and its subcategories.
Generic families of manifolds
- Euclidean space, R<sup>n</sup>
- n-sphere, S<sup>n</sup>
- n-torus, T<sup>n</sup>
- Real projective space, RP<sup>n</sup>
- Complex projective space, CP<sup>n</sup>
- Quaternionic projective space, HP<sup>n</sup>
- 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, S<sup>1</sup>
- Long line
- Real line, R
- Real projective line, RP<sup>1</sup> ≅ S<sup>1</sup>
2-manifolds
- Cylinder, S<sup>1</sup> × R
- Klein bottle, RP<sup>2</sup> # RP<sup>2</sup>
- Klein quartic (a genus 3 surface)
- Möbius strip
- Real projective plane, RP<sup>2</sup>
- Sphere, S<sup>2</sup>
- Surface of genus g
- Torus
- Double torus
3-manifolds
- 3-sphere, S<sup>3</sup>
- 3-torus, T<sup>3</sup>
- Poincaré homology sphere
- SO(3) ≅ RP<sup>3</sup>
- 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
- E<sub>8</sub> manifold
- Enriques surface
- Exotic R<sup>4</sup>
- Hirzebruch surface
- K3 surface
For more examples see 4-manifold.
Special types of manifolds
Manifolds related to spheres
- Brieskorn manifold
- Exotic sphere
- Homology sphere
- Homotopy sphere
- Lens space
- Spherical 3-manifold
Special classes of Riemannian manifolds
- Einstein manifold
- Ricci-flat manifold
- G<sub>2</sub> manifold
- Kähler manifold
- Calabi–Yau manifold
- Hyperkähler manifold
- Quaternionic Kähler manifold
- Riemannian symmetric space
- Spin(7) manifold
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
- Banach manifold
- Fréchet manifold
- Hilbert manifold