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Torsion, curvature and deflection \(d\)-tensors on \(J^1(T, M)\). (English) Zbl 0999.53024

Some special connections and their torsion and curvature tensors on manifolds of jets are investigated and their components are calculated in coordinates. The coordinate expressions of Olver’s prolongation (lifting) of vector fields on \(T\times M\) to \(J^1(T,M)\) are derived as well.

MSC:

53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
53C43 Differential geometric aspects of harmonic maps
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
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