GENERAL MATTER COUPLED N=2 SUPERGRAVITY

The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets with a generic gauging of the s calar manifold isometries is given, This extends the results already a vailable in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows us to cover th eories difficult to formulate within a superspace or tensor calculus a pproach. We provide the complete lagrangian and supersymmetry variatio ns with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Our results can be used to explore properties of theories admitting N=2 supergravity as low energy limit.