Summary: Geometrical concepts induced by a smooth mapping of manifolds with linear connections are introduced, especially the (higher order) covariant differentials of the mapping tangent to 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.
@article{701774,
title = {Connection induced geometrical concepts},
booktitle = {Proceedings of the 25th Winter School "Geometry and Physics"},
series = {GDML\_Books},
publisher = {Circolo Matematico di Palermo},
address = {Palermo},
year = {2006},
pages = {[153]-160},
mrnumber = {MR2287134},
zbl = {1113.58001},
url = {http://dml.mathdoc.fr/item/701774}
}
Musilová, Pavla; Musilová, Jana. Connection induced geometrical concepts, dans Proceedings of the 25th Winter School "Geometry and Physics", GDML_Books, (2006), pp. [153]-160. http://gdmltest.u-ga.fr/item/701774/