κ-Gauduchon Metrics On Almost Complex Manifold

Recently, the k-Gauduchon metrics on a compact complex manifold was intro-duced by J.Fu, Z.Wang and D. Wu [3], In this paper, we generalize this notion on a compact almost complex manifold and, as in [3], define the γk functions on the space of its hermitian metrics. We can get a semilinear elliptic equation which can be used to find k-Gauduchon metrics on a compact almost complex manifold. We discuss the exis-tence and uniquess of the solution to this equation and get the estimate for the solution, then we discuss two cases, respectively,γk=0and γk>0.