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Connection induced geometrical concepts. (English) Zbl 1113.58001
Čadek, Martin (ed.), The proceedings of the 25th winter school “Geometry and physics”, Srní, Czech Republic, January 15–22, 2006. Palermo: Circolo Matemático di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 79, 153-160 (2006).
Summary: Geometrical concepts induced by a smooth mapping $$f:M\to N$$ of manifolds with linear connections are introduced, especially the (higher order) covariant differentials of the mapping tangent to $$f$$ and the curvature of a corresponding tensor product connection. As an useful and physically meaningful consequence a basis of differential invariants for natural operators of such smooth mappings is obtained for metric connections. A relation to geometry of Riemannian manifolds is discussed.
For the entire collection see [Zbl 1103.53001].
##### MSC:
 58A20 Jets in global analysis 53B05 Linear and affine connections