Degenerate metrical -structure on vector bundles.
Differential pseudoconnections and field theories
Distinguished geodesics and jacobi fields on first order jet spaces
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.
Double groupoids and crossed modules