Connector (mathematics)
Encyclopedia
In mathematics
, a connector is a map which can be defined for a linear connection
and used to define the covariant derivative
on a vector bundle
from the linear connection.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a connector is a map which can be defined for a linear connection
Linear connection
In the mathematical field of differential geometry, the term linear connection can refer to either of the following overlapping concepts:* a connection on a vector bundle, often viewed as a differential operator ;* a principal connection on the frame bundle of a manifold or the induced connection...
and used to define the covariant derivative
Covariant derivative
In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given...
on a vector bundle
Vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X : to every point x of the space X we associate a vector space V in such a way that these vector spaces fit together...
from the linear connection.