# Dual connection

From Diffgeom

Revision as of 23:47, 4 April 2008 by Vipul (talk | contribs) (New page: ==Definition== Suppose <math>E</math> is a vector bundle over a differential manifold <math>M</math> and <math>\nabla</math> is a connection on <math>E</math>. The '''dual con...)

## Definition

Suppose is a vector bundle over a differential manifold and is a connection on . The **dual connection** to , denoted , is a connection on the dual vector bundle , defined as follows.

For any and , we have:

where

## Motivation

The definition of a dual connection is chosen in such a way that the bilinear form for evaluation:

satisfies the Leibniz rule. In other wors, we need to ensure that for and , we have: