Connections on tangent bundles of higher order associated to regular Lagrangians |
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| Authors: | Luis C de Andrés Manuel de León Paulo R Rodrigues |
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| Institution: | (1) Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, Bilbao, Spain;(2) Unidad de Matemáticas, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain;(3) Departamento de Geometría, Instituto de Matematica, Universidade Federal Fluminense, 24.000 Niteroi, R.J., Brazil |
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| Abstract: | Given a regular Lagrangian L of order k on M we show that there exists a canonical connection 
L
on T
2k–1
M whose paths are the solutions of the Euler-Lagrange equations for L. If L is the kinetic energy defined by a Riemannian metric then
L
is the Riemannian connection.Partially supported by Subdirección General de Cooperación Internacional, Programa de Cooperación Científica con Iberoamérica, SPAIN and CNPq-BRAZIL, Proc. 30.1115/79. |
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