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Connection induced geometrical concepts

Musilová, PavlaMusilová, Jana — 2006

Proceedings of the 25th Winter School "Geometry and Physics"

Summary: Geometrical concepts induced by a smooth mapping f : M 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.

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