The complete N=3 matter coupled supergravity

The complete N=3 matter coupling to supergravity is obtained in a geometrical framework. This coupling always exists if the 3n complex scalars of the n vector multiplets are co-ordinates of the Kaehler-grassmannian manifold SU(3,n)/SU(3)xSU(n)xU(1). Subgroups of SO(3,n)is contained inSU(3,n) of dimension 3+n can be gauged and give rise to a non-trivial scalar potential. The techniques used in this paper allow for the calculation of scalar potentials of extended supergravities in any dimension without explicit construction of the lagrangian. This opens the possibility of discussing patterns of partial supersymmetry and gauge symmetry breaking on a purely group-theoretical ground. (orig.)