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Einstein manifold. Ricci-flat manifold. G2 manifold. Kähler manifold. Calabi–Yau manifold. Hyperkähler manifold. Quaternionic Kähler manifold. Riemannian symmetric space. Spin (7) manifold.
Category of manifolds. Classification of manifolds. Closed manifold. Collapsing manifold. Collar neighbourhood. Complete manifold. Complex Lie group. Configuration space (mathematics) Conformally flat manifold.
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space.
In mathematics, the category of manifolds, often denoted Manp, is the category whose objects are manifolds of smoothness class Cp and whose morphisms are p -times continuously differentiable maps. This is a category because the composition of two Cp maps is again continuous and of class Cp. One is often interested only in Cp -manifolds modeled ...
Flat manifold. In mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles of a triangle add up to 180°.
Overview. Low-dimensional manifolds are classified by geometric structure; high-dimensional manifolds are classified algebraically, by surgery theory. "Low dimensions" means dimensions up to 4; "high dimensions" means 5 or more dimensions. The case of dimension 4 is somehow a boundary case, as it manifests "low dimensional" behaviour smoothly ...
The following is a list of named topologies or topological spaces, many of which are counterexamples in topology and related branches of mathematics. This is not a list of properties that a topology or topological space might possess; for that, see List of general topology topics and Topological property.
Topological manifold. In topology, a topological manifold is a topological space that locally resembles real n - dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds are topological manifolds by definition. Other types of manifolds are formed by ...
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