High Quality Content by WIKIPEDIA articles! In differential geometry, an Ehresmann connection (after the French mathematician Charles Ehresmann who first formalized this concept) is a version of the notion of a connection, which makes sense on any smooth fibre bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fibre bundle, but nevertheless, linear connections may be viewed as a special case. Another important special case of Ehresmann connections are principal connections on principal bundles, which are required to be equivariant in the principal Lie group action.