- In mathematics, a
holomorphic function is a complex-valued
function of one or more
complex variables that is
complex differentiable in a neighbourhood...
-
particularly concerned with
analytic functions of a
complex variable, that is,
holomorphic functions. The
concept can be
extended to
functions of
several complex...
-
algebraic geometry, a
formal holomorphic function along a
subvariety V of an
algebraic variety W is an
algebraic analog of a
holomorphic function defined in a...
- π : E → X is
holomorphic.
Fundamental examples are the
holomorphic tangent bundle of a
complex manifold, and its dual, the
holomorphic cotangent bundle...
-
every point p {\displaystyle p} of X {\displaystyle X} ,
there is a
holomorphic coordinate chart around p {\displaystyle p} in
which the
metric agrees...
- mathematics, in the
field of
complex geometry, a
holomorphic curve in a
complex manifold M is a non-constant
holomorphic map f from the
complex plane to M. Nevanlinna...
- line
integrals for
holomorphic functions in the
complex plane. Essentially, it says that if f ( z ) {\displaystyle f(z)} is
holomorphic in a
simply connected...
- 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...
- of one variable,
which is the case n = 1, the
functions studied are
holomorphic or
complex analytic so that, locally, they are
power series in the variables...
