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Some natural operations between connections on fibred manifolds

Doupovec, Miroslav, Vondra, Alexandr (1996)

Proceedings of the Winter School "Geometry and Physics"

Given a fibered manifold Y X , a 2-connection on Y means a section J 1 Y J 2 Y . The authors determine all first order natural operators transforming a 2-connection on Y and a classical linear connection on X into a connection on J 1 Y Y . (The proof implies that there is no first order natural operator transforming 2-connections on Y into connections on J 1 Y Y .) Using this result, the authors deduce several properties of characterizable connections on J 1 Y X .

Special connections on smooth 3-web manifolds

Vanžurová, Alena (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

For a three-web W of codimension n on a differentiable manifold M 2 n of dimension 2 n , the author studies the Chern connection and a family of parallelizing connections. The latter ones have a common property with the former: the web-distributions are parallel with respect to them.

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