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 List of topological spaces – List of concrete topologies and topological spaces
References