Nonlinear Connections in Superbundles and Locally Anisotropic Supergravity

The theory of locally anisotropic superspaces (supersymmetric generalizations of various types of Kaluza–Klein, Lagrange and Finsler spaces) is laid down. In this framework we perform the analysis of construction of the supervector bundles provided with nonlinear and distinguished connections and metric structures. Two models of locally anisotropic supergravity are proposed and studied in details.