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Another word for a C^infty (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...

A smooth structure on a topological manifold (also called a differentiable structure) is given by a smooth atlas of coordinate charts, i.e., the transition functions between ...

A smooth manifold with a Poisson bracket defined on its function space.

A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.

A semi-Riemannian manifold M=(M,g) is said to be Lorentzian if dim(M)>=2 and if the index I=I_g associated with the metric tensor g satisfies I=1. Alternatively, a smooth ...

A topological space M satisfying some separability (i.e., it is a T2-space) and countability (i.e., it is a paracompact space) conditions such that every point p in M has a ...

A complex manifold is a manifold M whose coordinate charts are open subsets of C^n and the transition functions between charts are holomorphic functions. Naturally, a complex ...

A smooth manifold M=(M,g) is said to be semi-Riemannian if the indexMetric Tensor Index of g is nonzero. Alternatively, a smooth manifold is semi-Riemannian provided that it ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...