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Fernando Etayo Gordejuela (1991)
Collectanea Mathematica
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We study the 2-jet bundle of mappings of the real plane into a manifold. We shall prove that there exists an imbedding of this 2-jet bundle into a suitable first order jet bundle, in such a way that its image is the set of fixed points of a canonical automorphism of the biggest jet bundle.
Iliev, Bozhidar Z. (2006)
International Journal of Mathematics and Mathematical Sciences
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Janyška, J., Modugno, M. (1996)
Archivum Mathematicum
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Daniel Canarutto (2004)
Rendiconti del Seminario Matematico della Università di Padova
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Marco Modugno (1989)
Časopis pro pěstování matematiky
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Antonella Cabras, Ivan Kolář (1995)
Czechoslovak Mathematical Journal
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Charles-Michel Marle (2007)
Banach Center Publications
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Around 1923, Élie Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers,...
Eduardo Martínez (1996)
Extracta Mathematicae
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Given a second order differential equation on a manifold we find necessary and sufficient conditions for the existence of a coordinate system in which the system is linear. The main tool to be used is a linear connection defined by the system of differential equations.