List of manifolds

This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see and its subcategories.

Generic families of manifolds

*Euclidean space, R^"n"
*"n"-sphere, "S"^"n"
*"n"-torus, T^"n"
*Real projective space, RP^"n"
*Complex projective space, CP^"n"
*Quaternionic projective space, HP^"n"
*Grassmann manifold
*Flag manifold
*Stiefel manifold

Lie groups provide more 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

*Real line, R
*Circle, "S"¹
*Real projective line, RP¹ ≅ "S"¹
*Long line

2-manifolds

*Sphere, "S"²
*Real projective plane, RP²
*Torus
*Klein bottle
*Cylinder
*Möbius strip
*Double torus
*Klein quartic (a genus 3 surface)

3-manifolds

*3-sphere, "S"³
*SO(3) ≅ RP³
*Poincaré homology sphere
*Whitehead manifold
*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."

pecial types of manifolds

Manifolds related to spheres

*Homology sphere
*Homotopy sphere
*Exotic sphere
*Milnor sphere
*Spherical 3-manifold
*Lens space

pecial classes of Riemannian manifolds

*Riemannian symmetric space
*Einstein manifold
**Ricci-flat manifold
*Kähler manifold
**Calabi-Yau manifold
**Hyperkähler manifold
*Quaternionic Kähler manifold
*"G"₂ manifold
*Spin(7) manifold

Categories of manifolds

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
*Symplectic manifold
*Almost complex manifold
*Lie group

Infinite-dimensional manifolds

*Hilbert manifold
*Banach manifold
*Fréchet manifold