Neha Patil (Editor)

List of manifolds

Updated on
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

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

Contents

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, RP1S1
  • 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
  • References

    List of manifolds Wikipedia


    Similar Topics
    The Rocks of Valpre (1935 film)
    Enzo Fileno Carabba
    Greg Norton (baseball)
    Topics
     
    B
    i
    Link
    H2
    L