In
mathematics, a connector is a map which can be defined for a
linear connection and used to define the
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 differ ...
on a
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 (for example X could be a topological space, a manifold, or an algebraic variety): to ev ...
from the linear connection.
Definition
Let ∇ be a connection on the tangent space TN of a smooth manifold N. For smooth mappings h:M→TN from any smooth manifold M, the connector K:TTN→TN satisfies :
∇ h = K○Th:TM→TN where Th:TM→TTN is the differential of h.
Connection (mathematics)
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