A Finslerian extension of the gravitational field (Q1082617)

The author has attempted a structural generalization of the gravitational field to Finsler spaces. A new Finsler metric \(g_{\lambda \kappa}(x,y)=\gamma_{\lambda \kappa}(x)+h_{\lambda \kappa}(y)\) is constructed by unifying the Riemannian metric of the external field, \(\gamma_{\lambda \kappa}(x)\) spanned by points \(\{\) \(x\}\) and the Riemannian metric of the internal field, \(h_{\lambda \kappa}(y)\) spanned by vectors \(\{\) \(y\}\). The connections with respect to the new metric is also determined.