Locally Anisotropic Supergravity and Gauge Gravity on Noncommutative Spaces

We outline the the geometry of locally anisotropic (la) superspaces and la-supergravity. The approach is backgrounded on the method of anholonomic superframes with associated nonlinear connection structure. Following the formalism of enveloping algebras and star product calculus we propose a model of gauge la-gravity on noncommutative spaces. The corresponding Seiberg-Witten maps are established which allow the definition of dynamics for a finite number of gravitational gauge field components on noncommutative spaces.