String and Metric–Affine Gravity

We develop the method of anholonomic frames with associated nonlinear connec-tion (in brief, N–connection) structure and show explicitly how geometries with lo-cal anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton geometry) can bemodeled in the metric–affine spaces. There are formulated the criteria when such gen-eralized Finsler metrics are effectively induced in the Einstein, teleparallel, Riemann–Cartan and metric–affine gravity. We argue that every generic off–diagonal metric(which can not be diagonalized by coordinate transforms) is related to specific N–connection configurations. We elaborate the concept of generalized Finsler–affinegeometry for spaces provided with arbitrary N–connection, metric and linear connec-tion structures and characterized by gravitational field strengths, i. e. by nontrivialN–connection curvature, Riemannian curvature, torsion and nonmetricity. We ap-ply a irreducible decomposition techniques (in our case with additional N–connectionsplitting) and study the dynamics of metric–affine gravity fields generating Finslerlike configurations. The classification of basic eleven classes of metric–affine spaceswith generic local anisotropy is presented. Pacs: 04.50.+h, 02.40.-k,MSC numbers: 83D05, 83C99, 53B20, 53C60