On Einstein m-th root metrics

In this paper, we prove that if the m  -th root metric F=ai1i2⋯im(x)yi1yi2⋯yimm is an Einstein metric, that is, Ric=(n−1)KF2Ric=(n−1)KF2, where K=K(x)K=K(x) is a scalar function, then K=0K=0.