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manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold,...

error in an earlier paper Whitehead (1934, theorem 3) where he incorrectly claimed that no such manifold exists. A contractible manifold is one that can continuously...

Berger's 1955 paper on the classification of Riemannian holonomy groups first raised the issue of the existence of non-symmetric manifolds with holonomy...

differential 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...

a closed connected two-dimensional manifold is fully characterized by its Betti numbers. As part of his 1895 paper Analysis Situs (announced in 1892)...

In mathematics, a differentiable manifold M {\displaystyle M} of dimension n is called parallelizable if there exist smooth vector fields { V 1 , … , V...

required the stronger assumption that the underlying closed Riemannian manifold has nonnegative sectional curvature and parallel Ricci tensor (such as...

In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible...

the Courant Institute in New York University, where he began work on manifolds with lower bounds on Ricci curvature. From there, he accepted a two-year...

mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle satisfying a...

In differential geometry, a G2 manifold or Joyce manifold is a seven-dimensional Riemannian manifold with holonomy group contained in G2. The group G...

Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in...

Manifold Garden is a puzzle video game developed by American artist William Chyr. It was released on Windows, macOS, and iOS on October 18, 2019. The player...

MathWorld Killing's Equation From MathWorld Killing and Twistor Spinors on Lorentzian Manifolds, (paper by Christoph Bohle) (postscript format) v t e...

In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface...

differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup...

1990 paper Special Geometry. The Higgs branch is a hyperkähler manifold as was shown by Luis Alvarez-Gaume and Daniel Freedman in their 1981 paper Geometrical...

explicit formula for the conformally invariant Green's function on a 4-manifold. In his paper with Jones, he studied the topology of the moduli space of SU(2)...

Allendoerfer and André Weil proved a special case for extrinsic manifolds. In a classic paper published in 1944, Shiing-Shen Chern proved the theorem in full...

the category of smooth manifolds. That is, E , B , {\displaystyle E,B,} and F {\displaystyle F} are required to be smooth manifolds and all the functions...