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mathematics, an analytic manifold, also known as a C ω {\displaystyle C^{\omega }} manifold, is a differentiable manifold with analytic transition maps...

In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in the complex coordinate...

differentiable manifolds are smooth and analytic manifolds. For smooth manifolds the transition maps are smooth, that is, infinitely differentiable. Analytic manifolds...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...

classification of (separable) one-dimensional analytic manifolds, which is more difficult than for differentiable manifolds). Again, any given C ∞ {\displaystyle...

bounded analytic function can become Analytic continuation, a technique to extend the domain of definition of a given analytic function Analytic manifold, a...

Topological manifold, a topological space which is a locally Euclidean Hausdorff space Almost complex manifold Algebraic manifold Analytic manifold Calabi–Yau...

complex manifolds and complex projective varieties ( C P n {\displaystyle \mathbb {CP} ^{n}} ) and has a different flavour to complex analytic geometry...

that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles...

Categories of Manifolds Affine manifold Analytic manifold Complex manifold Differentiable (smooth) manifold Piecewise linear manifold Lipschitz manifold Topological...

An analytic space is a generalization of an analytic manifold that allows singularities. An analytic space is a space that is locally the same as an analytic...

In mathematics, a Banach manifold is a manifold modeled on Banach spaces. Thus it is a topological space in which each point has a neighbourhood homeomorphic...

complex analytic variety or complex analytic space is a generalization of a complex manifold that allows the presence of singularities. Complex analytic varieties...

abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds. For example, in the Hamiltonian formulation of...

Riemannian metric on a smooth manifold is analytic, in the sense that harmonic coordinates define a compatible analytic structure, and the local representation...

almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. Every complex manifold is an almost...

in pure algebraic geometry, where analytic results in the complex setting such as Hodge theory of Kähler manifolds inspire understanding of Hodge structures...

in continuous and smooth manifolds, but not in analytic manifolds. Thus for an open cover of an analytic manifold, an analytic partition of unity subordinate...

(maximal) analytic continuation of an analytic function. In the GAGA set of analogies, Stein manifolds correspond to affine varieties. Stein manifolds are in...

p-adic analytic manifolds, rigid analytic spaces admit meaningful notions of analytic continuation and connectedness. The basic rigid analytic object...