Local anisotropic Yang-Mils and gage gravitational fields

A geometrical treatment of gauge theories for semisimple and non semisimple groups is given in the framework of fiber bundles on bases with local anisotropy. We consider the general case of locally anisotropic spaces, the so-called generalized Lagrange spaces, GL-spaces, and the Miron's almost Hermitian model of GL-spaces, H2n-spaces. We formulate the Young-Mills theory on H2n-spaces and provide that H2n-gravity can be equivalently rewritten as a gauge-like theory in the bundle of local affine frames, adapted to nonlinear connection on the corresponding GL-space, on base space H2n. By using a nonlinear variant of de Sitter gauge gravity we construct solutions for locally anisotropic gravitational instantons. (Author)