Canonical Nonlinear Connections on Jet Bundles of First Order

الأصل · EN

The aim of this paper is to open the problem of construction of a nonlinear connection Γ=(M⁽ⁱ⁾₍α₎ᵦ, N⁽ⁱ⁾₍α₎ⱼ) on the jet bundle of first order J¹(T,M), which to be canonically produced by a Kronecker product vertical metrical d-tensor G⁽α⁾⁽β⁾₍ᵢ₎₍ⱼ₎=hαβgij, possibly provided by multi-time dependent quadratic Lagrangians coming from various branches of theoretical physics: bosonic strings theory, electrodynamics or elasticity.