Generalized curvature and the equations of supergravity

Abstract: It is known that, for zero fermionic sector, , the bosonic equations of Cremmer–Julia–Scherk eleven-dimensional supergravity can be collected in a compact expression, , which is a condition on the curvature of the generalized connection w. In this Letter we show that the equation , where is the covariant derivative for the generalized connection w, collects all the bosonic equations of supergravity when the gravitino is nonvanishing, . [Copyright &y& Elsevier]