Connector (mathematics)

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.

## 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.

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