Antisymmetric tensor matter fields in a curved space-time

An analysis about the antisymmetric tensor matter fields Avdeev-Chizhov theory in a curved space-time is performed. We show, in a curved spacetime, that the Avdeev-Chizhov theory can be seen as a kind of a $\lambda\phi^{4}$ theory for a "complex self-dual" field. This relationship between Avdeev-Chizhov theory and $\lambda\phi^{4}$ theory simplify the study of tensor matter fields in a curved space-time. The energy-momentum tensor for matter fields is computed.