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We consider the geometrical formulation in central charge superspace of theN=4 supergravity containing an antisymmetric tensor gauge field. The theory ison-shell, so clearly, the constraints used for the identification of themultiplet together with the superspace Bianchi identities imply equations ofmotion for the component fields. We deduce these equations of motion in termsof supercovariant quantities and then, we give them in terms of componentfields. These equations of motion, deduced from the geometry, without supposingthe existence of a Lagrangian, are found to be the same as those derived fromthe Lagrangian given in the component formulation of this N=4 supergravitymultiplet by Nicolai and Townsend.Comment: 18 pages ; typos correcte

Equation of motion forN= 4 supergravity with antisymmetric tensor from its geometric description in central charge superspace