complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients. Complex forms...

In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The...

for applications of these ideas. Almost complex manifold Complex manifold Complex differential form Complex conjugate vector space Hermitian structure...

has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric. Such forms are called harmonic. The theory...

normal form by a suitable choice of the coordinate system. Complex differential geometry is the study of complex manifolds. An almost complex manifold...

two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable...

In complex geometry, the term positive form refers to several classes of real differential forms of Hodge type (p, p). Real (p,p)-forms on a complex manifold...

algebraic geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept...

).} In complex differential geometry, the Laplace operator (also known as the Laplacian) is defined in terms of the complex differential forms. ∂ f =...

\omega ,J)} admits a large number of operators on its algebra of complex differential forms Ω ( X ) := ⨁ k ≥ 0 Ω k ( X , C ) = ⨁ p , q ≥ 0 Ω p , q ( X ) {\displaystyle...

Galois theory, differential geometry and algebraic geometry. They can be defined more generally in abelian categories. A chain complex ( A ∙ , d ∙ ) {\displaystyle...

a mathematical lemma about the de Rham cohomology class of a complex differential form. The ∂ ∂ ¯ {\displaystyle \partial {\bar {\partial }}} -lemma...

condition for a closed differential form to be exact (while an exact form is necessarily closed). Precisely, it states that every closed p-form on an open ball...

linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written in the form a 0...

In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. The notion was introduced...

In differential geometry and complex geometry, a complex manifold is a manifold with a complex structure, that is an atlas of charts to the open unit...

In mathematics, differential forms on a Riemann surface are an important special case of the general theory of differential forms on smooth manifolds...

boundary operator in a chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold. It should be distinguished...

manifolds. — Terence Tao, Differential Forms and Integration The de Rham complex is the cochain complex of differential forms on some smooth manifold M...

commander Dorotheos Dbar (born 1972), an Abkhazian religious figure Complex differential form, in mathematics DBAR problem, also in mathematics ∂ ¯ {\displaystyle...

A differential amplifier is a type of electronic amplifier that amplifies the difference between two input voltages but suppresses any voltage common to...

In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first...

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions...

In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold...

everywhere-regular differential 1-forms. Given a complex manifold M, a differential of the first kind ω is therefore the same thing as a 1-form that is everywhere...

for the operator ∂ ¯ {\displaystyle {\bar {\partial }}} (see complex differential form) in PDE theory, to extend Hodge theory and the n-dimensional Cauchy–Riemann...

of complex differential forms of degree (p,q). Let Ωp,q be the vector bundle of complex differential forms of degree (p,q). In the article on complex forms...

field Tensor field Differential form Exterior derivative Lie derivative pullback (differential geometry) pushforward (differential) jet (mathematics)...

mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian...

or geometric space. Explicitly, a differential graded algebra is a graded associative algebra with a chain complex structure that is compatible with the...