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72 relations: Almost complex manifold, Almost symplectic manifold, Analytic manifold, Banach manifold, Calabi–Yau manifold, Calibrated geometry, Circle, Complex manifold, Complex projective space, Contact geometry, CR manifold, Cylinder, Differentiable manifold, E8 manifold, Einstein manifold, Euclidean space, Exotic R4, Exotic sphere, Finsler manifold, Fréchet manifold, G2 manifold, Generalized flag variety, Genus (mathematics), Genus-three surface, Genus-two surface, Grassmannian, Hermitian manifold, Hilbert manifold, Homology sphere, Homotopy sphere, Hyperkähler manifold, Kähler manifold, Klein bottle, Klein quartic, Lens space, Lie group, List of geometric topology topics, List of Lie groups topics, List of simple Lie groups, Long line (topology), Manifold, Möbius strip, N-sphere, Piecewise linear manifold, Pseudo-Riemannian manifold, Quaternion-Kähler manifold, Quaternionic projective space, Real line, Real projective line, Real projective plane, ..., Real projective space, Ricci-flat manifold, Riemannian manifold, Rotation group SO(3), Sasakian manifold, Solid Klein bottle, Solid torus, Sphere, Spherical 3-manifold, Spin structure, Spin(7)-manifold, Stiefel manifold, Symmetric space, Symplectic manifold, Table of Lie groups, Topological manifold, Torus, Weeks manifold, Whitehead manifold, 3-manifold, 3-sphere, 4-manifold. Expand index (22 more) »
Almost complex manifold
In mathematics, an almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space.
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Almost symplectic manifold
In differential geometry, an almost symplectic structure on a differentiable manifold M is a two-form ω on M that is everywhere non-singular.
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Analytic manifold
In mathematics, an analytic manifold is a topological manifold with analytic transition maps.
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Banach manifold
In mathematics, a Banach manifold is a manifold modeled on Banach spaces.
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Calabi–Yau manifold
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics.
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Calibrated geometry
In the mathematical field of differential geometry, a calibrated manifold is a Riemannian manifold (M,g) of dimension n equipped with a differential ''p''-form φ (for some 0 ≤ p ≤ n) which is a calibration in the sense that.
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Circle
A circle is a simple closed shape.
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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Complex projective space
In mathematics, complex projective space is the projective space with respect to the field of complex numbers.
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Contact geometry
In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a condition called 'complete non-integrability'.
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CR manifold
In mathematics, a CR manifold is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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E8 manifold
In mathematics, the E8 manifold is the unique compact, simply connected topological 4-manifold with intersection form the ''E''8 lattice.
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Einstein manifold
In differential geometry and mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Exotic R4
In mathematics, an exotic R4 is a differentiable manifold that is homeomorphic but not diffeomorphic to the Euclidean space R4.
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Exotic sphere
In differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere.
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Finsler manifold
In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold where a (possibly asymmetric) Minkowski norm is provided on each tangent space, allowing to define the length of any smooth curve as Finsler manifolds are more general than Riemannian manifolds since the tangent norms need not be induced by inner products.
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Fréchet manifold
In mathematics, in particular in nonlinear analysis, a Fréchet manifold is a topological space modeled on a Fréchet space in much the same way as a manifold is modeled on a Euclidean space.
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G2 manifold
In differential geometry, a G2 manifold is a seven-dimensional Riemannian manifold with holonomy group equal to ''G''2.
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Generalized flag variety
In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold.
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Genus (mathematics)
In mathematics, genus (plural genera) has a few different, but closely related, meanings.
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Genus-three surface
In geometry, a genus-three surface is a smooth closed surface with three holes, or, in other words, a surface of genus three.
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Genus-two surface
In mathematics, a genus-two surface (also known as a double torus or two-holed torus) is a surface formed by the connected sum of two tori.
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Grassmannian
In mathematics, the Grassmannian is a space which parametrizes all -dimensional linear subspaces of the n-dimensional vector space.
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Hermitian manifold
In mathematics, and more specifically in differential geometry, a Hermitian manifold is the complex analogue of a Riemannian manifold.
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Hilbert manifold
In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces.
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Homology sphere
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1.
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Homotopy sphere
In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere.
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Hyperkähler manifold
In differential geometry, a hyperkähler manifold is a Riemannian manifold of dimension 4k and holonomy group contained in Sp(''k'') (here Sp(k) denotes a compact form of a symplectic group, identified with the group of quaternionic-linear unitary endomorphisms of a k-dimensional quaternionic Hermitian space).
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Kähler manifold
In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure.
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Klein bottle
In topology, a branch of mathematics, the Klein bottle is an example of a non-orientable surface; it is a two-dimensional manifold against which a system for determining a normal vector cannot be consistently defined.
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Klein quartic
In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus with the highest possible order automorphism group for this genus, namely order orientation-preserving automorphisms, and automorphisms if orientation may be reversed.
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Lens space
A lens space is an example of a topological space, considered in mathematics.
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Lie group
In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
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List of geometric topology topics
This is a list of geometric topology topics, by Wikipedia page.
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List of Lie groups topics
This is a list of Lie group topics, by Wikipedia page.
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List of simple Lie groups
In mathematics, the simple Lie groups were first classified by Wilhelm Killing and later perfected by Élie Cartan.
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Long line (topology)
In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer".
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Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
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Möbius strip
The Möbius strip or Möbius band, also spelled Mobius or Moebius, is a surface with only one side (when embedded in three-dimensional Euclidean space) and only one boundary.
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N-sphere
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
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Piecewise linear manifold
In mathematics, a piecewise linear (PL) manifold is a topological manifold together with a piecewise linear structure on it.
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Pseudo-Riemannian manifold
In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.
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Quaternion-Kähler manifold
In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some n\geq 2.
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Quaternionic projective space
In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by and is a closed manifold of (real) dimension 4n.
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Real line
In mathematics, the real line, or real number line is the line whose points are the real numbers.
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Real projective line
In geometry, a real projective line is an extension of the usual concept of line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity".
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Real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface.
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Real projective space
In mathematics, real projective space, or RPn or \mathbb_n(\mathbb), is the topological space of lines passing through the origin 0 in Rn+1.
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Ricci-flat manifold
In mathematics, Ricci-flat manifolds are Riemannian manifolds whose Ricci curvature vanishes.
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Riemannian manifold
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.
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Rotation group SO(3)
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition.
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Sasakian manifold
In differential geometry, a Sasakian manifold (named after Shigeo Sasaki) is a contact manifold (M,\theta) equipped with a special kind of Riemannian metric g, called a Sasakian metric.
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Solid Klein bottle
In mathematics, a solid Klein bottle is a three-dimensional topological space (a 3-manifold) whose boundary is the Klein bottle.
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Solid torus
In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle.
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Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").
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Spherical 3-manifold
In mathematics, a spherical 3-manifold M is a 3-manifold of the form where \Gamma is a finite subgroup of SO(4) acting freely by rotations on the 3-sphere S^3.
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Spin structure
In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.
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Spin(7)-manifold
In mathematics, a Spin(7)-manifold is an eight-dimensional Riemannian manifold with the exceptional holonomy group Spin(7).
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Stiefel manifold
In mathematics, the Stiefel manifold Vk(Rn) is the set of all orthonormal ''k''-frames in Rn.
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Symmetric space
In differential geometry, representation theory and harmonic analysis, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point.
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Symplectic manifold
In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form, ω, called the symplectic form.
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Table of Lie groups
This article gives a table of some common Lie groups and their associated Lie algebras.
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Topological manifold
In topology, a branch of mathematics, a topological manifold is a topological space (which may also be a separated space) which locally resembles real n-dimensional space in a sense defined below.
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Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
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Weeks manifold
In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead link.
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Whitehead manifold
In mathematics, the Whitehead manifold is an open 3-manifold that is contractible, but not homeomorphic to R3.
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3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.
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3-sphere
In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.
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4-manifold
In mathematics, a 4-manifold is a 4-dimensional topological manifold.
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References
[1] https://en.wikipedia.org/wiki/List_of_manifolds
