abelian differential
1Differential of the first kind — In mathematics, differential of the first kind is a traditional term used in the theories of Riemann surfaces (more generally, complex manifolds) and algebraic curves (more generally, algebraic geometry), for everywhere regular differential 1… …
2Differential (calculus) — In mathematics, and more specifically, in differential calculus, the term differential has several interrelated meanings.Basic notions* In traditional approaches to calculus, the differential (e.g. dx, dy, dt, etc...) of a function represents an… …
3Abelian — Abelian, in mathematics, is used in many different definitions, named after Norwegian mathematician Niels Henrik Abel:In group theory:*Abelian group, a group in which the binary operation is commutative **Category of abelian groups Ab has abelian …
4Differential form — In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better[further explanation needed] definition… …
5Abelian variety — In mathematics, particularly in algebraic geometry, complex analysis and number theory, an Abelian variety is a projective algebraic variety that is at the same time an algebraic group, i.e., has a group law that can be defined by regular… …
6Differential (mathematics) — In mathematics, the term differential has several meanings. Contents 1 Basic notions 2 Differential geometry 3 Algebraic geometry 4 Other meanings …
7Abelian integral — In mathematics, an abelian integral in Riemann surface theory is a function related to the indefinite integral of a differential of the first kind. Suppose we are given a Riemann surface S and on it a differential 1 form ω that is everywhere… …
8Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …
9Quadratic differential — In mathematics, a quadratic differential is a form on a Riemann surface that locally looks like the square of an abelian differential. It has (at least) two other interpretations that are useful in the study of Riemann surfaces: * a flat… …
10Ordinary differential equation — In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable. A simple example is Newton s second law of… …
