Conformally Minkowski type spaces and certain \(d\)-connections in a Miron space (Q1891440)

The dual (via Legendre morphism) of a Finsler space \(F^n = (M,F)\) is a space (called Miron space) \(\zeta^n = (M, H(x, p))\), where \(H : T^* M \to \mathbb{R}\) is a regular Hamiltonian, 2-homogeneous with respect to \(p_i\). For these spaces one determines a class of connections which have non vanishing \(h\)- and \(v\)-torsions and have a prescribed deflection tensor field. The conformal transformation \(\overline {H} (x,p) = e^{2 \sigma (x)} H(x,p)\) and the resulting conformal invariants are studied, too. The main result consists in establishing necessary and sufficient conditions for a space \(\zeta^n\) to be conformally Minkowski.