- In mathematics, a
holomorphic function is a complex-valued
function of one or more
complex variables that is
complex differentiable in a neighbourhood...
- ^{n}} are
holomorphically separable, in particular, all
domains in C n {\displaystyle \mathbb {C} ^{n}} and all
Stein manifolds. A
holomorphically separable...
-
polynomially convex hull
contains the
holomorphically convex hull. The
domain G {\displaystyle G} is
called holomorphically convex if for
every compact subset...
- {\displaystyle f} of a
complex variable z {\displaystyle z} : is said to be
holomorphic at a
point a {\displaystyle a} if it is
differentiable at
every point...
-
under the name
holomorphically symplectic manifolds. The
holonomy group of any Calabi–Yau
metric on a
simply connected compact holomorphically symplectic...
- π : E → X is
holomorphic.
Fundamental examples are the
holomorphic tangent bundle of a
complex manifold, and its dual, the
holomorphic cotangent bundle...
- functions) are a
family of
functions closely related to but
distinct from
holomorphic functions. A
function of the
complex variable z {\displaystyle z} defined...
- {\displaystyle \mathbb {C} ^{n}} , such that the
transition maps are
holomorphic. The term "complex manifold" is
variously used to mean a
complex manifold...
-
particularly concerned with
analytic functions of a
complex variable, that is,
holomorphic functions. The
concept can be
extended to
functions of
several complex...
- {\displaystyle X} is
holomorphically convex, i.e. for
every compact subset K ⊂ X {\displaystyle K\subset X} , the so-called
holomorphically convex hull, K ¯...
