Analytic manifold
Encyclopedia
In mathematics
, an analytic manifold is a topological manifold
with analytic
transition maps. Every complex manifold
is an analytic manifold.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an analytic manifold is a topological manifold
Topological manifold
In mathematics, a topological manifold is a topological space which looks locally like Euclidean space in a sense defined below...
with analytic
Analytic function
In mathematics, 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, categories that are similar in some ways, but different in others...
transition maps. Every complex manifold
Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic....
is an analytic manifold.