Displaying similar documents to “Synge-Beil and Riemann-Jacobi jet structures with applications to physics.”

Distinguished geodesics and jacobi fields on first order jet spaces

Vladimir Balan, Nicoleta Voicu (2004)

Open Mathematics

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In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.

From Euler-Lagrange equations to canonical nonlinear connections

Mircea Neagu (2006)

Archivum Mathematicum

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The aim of this paper is to construct a canonical nonlinear connection Γ = ( M ( α ) β ( i ) , N ( α ) j ( i ) ) on the 1-jet space J 1 ( T , M ) from the Euler-Lagrange equations of the quadratic multi-time Lagrangian function L = h α β ( t ) g i j ( t , x ) x α i x β j + U ( i ) ( α ) ( t , x ) x α i + F ( t , x ) .