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

Neagu, Mircea; Udrişte, Constantin

Balkan J. Geom. Appl. 6, No. 1, 29-44 (2001).

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.

Reviewer: A.Szybiak (Waterloo/Ontario)

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)

Keywords:

\(l\)-jet fibre bundle; \(\Gamma\)-linear connection; nonlinear connection; torsion and curvature; deflection \(d\)-tensors