List of manifolds

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, RP¹ ≅ S¹

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

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.

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