or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose...

(U_{1}\cap U_{2})\to \psi (U_{1}\cap U_{2})} is a biholomorphism. Notice that since every biholomorphism is a diffeomorphism, and C n {\displaystyle \mathbb...

holomorphic. At this time, ϕ {\displaystyle \phi } is called a U, V biholomorphism also, we say that U and V are biholomorphically equivalent or that they...

a biholomorphisms is locally in Γ, then it too is in Γ. The pseudogroup is said to be transitive if, given z and w in C, there is a biholomorphism f in...

compact Hermitian symmetric spaces: K is the isometry group, and G is the biholomorphism group of M. Over the real numbers, a real flag manifold is also called...

[1:x_{1}:\dots :x_{n}]} of the projective space thus defines the required biholomorphism. This model is the equivalent of the Poincaré disk model. Unlike the...

\mathbb {C} } , and assume that f : U → V {\displaystyle f:U\to V} is a biholomorphism. Then f {\displaystyle f} and f − 1 {\displaystyle f^{-1}} have antiderivatives...

collection of all local Ck diffeomorphisms on Rn form a pseudogroup. All biholomorphisms between open sets in Cn form a pseudogroup. More examples include:...

bounded symmetric domain if for every x in Ω, there is an involutive biholomorphism σx of Ω for which x is an isolated fixed point. The Harish-Chandra embedding...

anti-biholomorphic if they are homotopic to each other; the biholomorphism (or anti-biholomorphism) is precisely the harmonic map produced as the limit of...