A note on a relation between the Killing spinor and Einstein equations

It is shown that, under certain conditions, the existence of a Killing spinor on a bosonic background of a supergravity theory implies that the Einstein equations are also satisfied. As an application of the theorem, we obtain a new black fivebrane solution of D=11 supergravity, which has $K3\times R$ topology and preserves 1/4'th supersymmetries of the theory.