Yang-Mills fields and gauge gravity on generalized Lagrange and Finsler spaces (Q1903072)

In the framework of the theory of linear connections in vector bundles (with semisimple structural groups) on generalized Lagrange spaces, a geometrical approach to interactions of Yang-Mills fields on spaces with local anisotropy is formulated. The geometrical formalism is extended in a manner including theories with nonsemisimple groups which permit a unique fiber bundle treatment for both locally anisotropic Yang-Mills and gravitational interactions. One of the most important results of the paper is formulated as a theorem stating that almost Hermitian Lagrange gravity -- described in \textit{R. Miron} and \textit{M. Anastasiei} [The geometry of Lagrange spaces: theory and applications. Fundamental Theories of Physics, 59, Dordrecht: Kluwer Academic Publishers (1994; Zbl 0831.53001)], is equivalent to a gaugelike theory in the bundle of affine adapted frames on generalized Lagrange spaces.