Locally Conformal K¨ahler and Hermitian Yang-Mills Metrics

The author shows that if a locally conformal K¨ahler metric is Hermitian YangMills with respect to itself with Einstein constant c ≤ 0, then it is a K¨ahler-Einstein metric.In the case of c > 0, some identities on torsions and an inequality on the second Chern number are derived.