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 a complex structure, that is an atlas of charts to the open unit disc...

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...

In mathematics, the Prüfer manifold or Prüfer surface is a 2-dimensional Hausdorff real analytic manifold that is not paracompact. It was introduced by...

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

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

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...

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

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

geometry deals with complex manifolds and the more general analytic spaces defined locally by the vanishing of analytic functions of several complex...

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...

mathematics, dianalytic manifolds are possibly non-orientable generalizations of complex analytic manifolds. A dianalytic structure on a manifold is given by an...

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

is an analytic manifold (i.e. infinitely differentiable and charts are expressible as power series), and γ {\displaystyle \gamma } is an analytic map,...

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...

for a group acting on a complex-analytic manifold. Suppose a group G {\displaystyle G} acts on a complex-analytic manifold X {\displaystyle X} . Then, G...

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

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

sheaf of differentiable functions on a differentiable manifold is fine, in contrast with the analytic case. The functions below are generally used to build...

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

important) class of pro-p groups is the p-adic analytic groups: groups with the structure of an analytic manifold over Q p {\displaystyle \mathbb {Q} _{p}}...

extends naturally to functions on a complex curve, that is complex analytic manifold of dimension one (over the complex numbers). The simplest examples...

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

Franz (1935) and Georges de Rham (1936). Analytic torsion (or Ray–Singer torsion) is an invariant of Riemannian manifolds defined by Daniel B. Ray and Isadore...

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

an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions...

In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological...

and by others including Eugenio Beltrami who studied many analytic questions on manifolds. In 1899 Luigi Bianchi produced his Lectures on differential...