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, 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 Double 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 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 G2 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

See also

References