Complex manifolds

Riemannian manifold with SU(n) holonomy

manifold with an atlas of charts to the open unit disk in ℂⁿ, such that the transition maps are holomorphic

smooth manifold carrying compatible complex, Riemannian, and symplectic structures

study of complex manifolds and several complex variables

Kähler–Einstein metric on a complex projective space

holomorphically convex and holomorphically separable complex manifold

differential form on a manifold which is permitted to have complex coefficients

Mathematical term

finite-type sheaf F of modules over a ringed space such that the kernel of a surjective morphism from a finite direct sum of the structure sheaf onto it is also of finite type

the space of lines in a complex vector space

right|thumb|The complex exponential function mapping biholomorphically a rectangle to a quarter-annulus. In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic.

complex vector bundle on a complex manifold with biholomorphic transition maps

smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation

algorithm in algebraic geometry

In mathematics, the complexification of a vector space over the field of real numbers (a "real vector space") yields a vector space over the complex number field, obtained by formally extending the scaling of vectors by real numbers to include their scaling ("multiplication") by complex numbers. Any basis for (a space over the real numbers) may also serve as a basis for over the complex numbers.

Riemannian manifold with Sp(n) holonomy, or equivalently with an S² family of Kähler structures

Space in Twistor theory

duality for holomorphic vector bundles on a compact complex manifold induced by a dualizing sheaf