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Lagrangians and Euler morphisms from connections on the frame bundle. (English) Zbl 1291.53034

Herdeiro, Carlos (ed.) et al., XIX international fall workshop on geometry and physics, Porto, Portugal, September 6–9, 2010. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0918-7/pbk). AIP Conference Proceedings 1360, 139-144 (2011).
Summary: We classify all natural operators transforming torsion free classical linear connections \(\nabla\) on \(m\)-dimensional manifolds \(M\) into \(r\)th order Lagrangians \(\lambda(\nabla)\) and Euler morphisms \(E(\nabla)\) on the linear frame bundle \(P^1M\). We also briefly write how this classification result can be generalized on higher order frame bundles \(P^kM\) instead of \(P^1M\).
For the entire collection see [Zbl 1228.81023].

MSC:

53C05 Connections (general theory)
58A32 Natural bundles
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