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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. Manifolds of a specific dimension 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. Special types of manifolds 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 Categories of manifolds The Wikibook Topology has a page on the topic of: Categories of Manifolds See also: :Category:Structures on 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 Contact manifold Complex manifold Almost complex manifold Symplectic manifold Almost symplectic manifold Hermitian manifold Kahler manifold Hyperkahler manifold Calibrated manifold CR manifold Spin manifold Sasakian manifold Lie group Infinite-dimensional manifolds Hilbert manifold Banach manifold Fréchet manifold |
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